Tangent Lines and Lipschitz Differentiability Spaces

We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differenti...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Cavalletti Fabio [verfasserIn] Rajala Tapio [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	metric geometry lipschitz differentiability spaces tangent of metric spaces ricci curvature

Übergeordnetes Werk:	In: Analysis and Geometry in Metric Spaces - De Gruyter, 2015, 4(2016), 1
Übergeordnetes Werk:	volume:4 ; year:2016 ; number:1

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1515/agms-2016-0004

Katalog-ID:	DOAJ054770149

Internformat


LEADER	01000caa a22002652 4500
001	DOAJ054770149
003	DE-627
005	20230308184118.0
007	cr uuu---uuuuu
008	230227s2016 xx \|\|\|\|\|o 00\| \|\|eng c
024	7		\|a 10.1515/agms-2016-0004 \|2 doi
035			\|a (DE-627)DOAJ054770149
035			\|a (DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5
040			\|a DE-627 \|b ger \|c DE-627 \|e rakwb
041			\|a eng
050		0	\|a QA299.6-433
100	0		\|a Cavalletti Fabio \|e verfasserin \|4 aut
245	1	0	\|a Tangent Lines and Lipschitz Differentiability Spaces
264		1	\|c 2016
336			\|a Text \|b txt \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space.
650		4	\|a metric geometry
650		4	\|a lipschitz differentiability spaces
650		4	\|a tangent of metric spaces
650		4	\|a ricci curvature
653		0	\|a Analysis
700	0		\|a Rajala Tapio \|e verfasserin \|4 aut
773	0	8	\|i In \|t Analysis and Geometry in Metric Spaces \|d De Gruyter, 2015 \|g 4(2016), 1 \|w (DE-627)777285061 \|w (DE-600)2753702-X \|x 22993274 \|7 nnns
773	1	8	\|g volume:4 \|g year:2016 \|g number:1
856	4	0	\|u https://doi.org/10.1515/agms-2016-0004 \|z kostenfrei
856	4	0	\|u https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5 \|z kostenfrei
856	4	0	\|u https://doi.org/10.1515/agms-2016-0004 \|z kostenfrei
856	4	2	\|u https://doaj.org/toc/2299-3274 \|y Journal toc \|z kostenfrei
912			\|a GBV_USEFLAG_A
912			\|a SYSFLAG_A
912			\|a GBV_DOAJ
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_95
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 4 \|j 2016 \|e 1

Indexfelder

author_variant	c f cf r t rt
matchkey_str	article:22993274:2016----::agnlnsnlpcizifrn
hierarchy_sort_str	2016
callnumber-subject-code	QA
publishDate	2016
allfields	10.1515/agms-2016-0004 doi (DE-627)DOAJ054770149 (DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5 DE-627 ger DE-627 rakwb eng QA299.6-433 Cavalletti Fabio verfasserin aut Tangent Lines and Lipschitz Differentiability Spaces 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space. metric geometry lipschitz differentiability spaces tangent of metric spaces ricci curvature Analysis Rajala Tapio verfasserin aut In Analysis and Geometry in Metric Spaces De Gruyter, 2015 4(2016), 1 (DE-627)777285061 (DE-600)2753702-X 22993274 nnns volume:4 year:2016 number:1 https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5 kostenfrei https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/toc/2299-3274 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2016 1
spelling	10.1515/agms-2016-0004 doi (DE-627)DOAJ054770149 (DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5 DE-627 ger DE-627 rakwb eng QA299.6-433 Cavalletti Fabio verfasserin aut Tangent Lines and Lipschitz Differentiability Spaces 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space. metric geometry lipschitz differentiability spaces tangent of metric spaces ricci curvature Analysis Rajala Tapio verfasserin aut In Analysis and Geometry in Metric Spaces De Gruyter, 2015 4(2016), 1 (DE-627)777285061 (DE-600)2753702-X 22993274 nnns volume:4 year:2016 number:1 https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5 kostenfrei https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/toc/2299-3274 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2016 1
allfields_unstemmed	10.1515/agms-2016-0004 doi (DE-627)DOAJ054770149 (DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5 DE-627 ger DE-627 rakwb eng QA299.6-433 Cavalletti Fabio verfasserin aut Tangent Lines and Lipschitz Differentiability Spaces 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space. metric geometry lipschitz differentiability spaces tangent of metric spaces ricci curvature Analysis Rajala Tapio verfasserin aut In Analysis and Geometry in Metric Spaces De Gruyter, 2015 4(2016), 1 (DE-627)777285061 (DE-600)2753702-X 22993274 nnns volume:4 year:2016 number:1 https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5 kostenfrei https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/toc/2299-3274 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2016 1
allfieldsGer	10.1515/agms-2016-0004 doi (DE-627)DOAJ054770149 (DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5 DE-627 ger DE-627 rakwb eng QA299.6-433 Cavalletti Fabio verfasserin aut Tangent Lines and Lipschitz Differentiability Spaces 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space. metric geometry lipschitz differentiability spaces tangent of metric spaces ricci curvature Analysis Rajala Tapio verfasserin aut In Analysis and Geometry in Metric Spaces De Gruyter, 2015 4(2016), 1 (DE-627)777285061 (DE-600)2753702-X 22993274 nnns volume:4 year:2016 number:1 https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5 kostenfrei https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/toc/2299-3274 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2016 1
allfieldsSound	10.1515/agms-2016-0004 doi (DE-627)DOAJ054770149 (DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5 DE-627 ger DE-627 rakwb eng QA299.6-433 Cavalletti Fabio verfasserin aut Tangent Lines and Lipschitz Differentiability Spaces 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space. metric geometry lipschitz differentiability spaces tangent of metric spaces ricci curvature Analysis Rajala Tapio verfasserin aut In Analysis and Geometry in Metric Spaces De Gruyter, 2015 4(2016), 1 (DE-627)777285061 (DE-600)2753702-X 22993274 nnns volume:4 year:2016 number:1 https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5 kostenfrei https://doi.org/10.1515/agms-2016-0004 kostenfrei https://doaj.org/toc/2299-3274 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 4 2016 1
language	English
source	In Analysis and Geometry in Metric Spaces 4(2016), 1 volume:4 year:2016 number:1
sourceStr	In Analysis and Geometry in Metric Spaces 4(2016), 1 volume:4 year:2016 number:1
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	metric geometry lipschitz differentiability spaces tangent of metric spaces ricci curvature Analysis
isfreeaccess_bool	true
container_title	Analysis and Geometry in Metric Spaces
authorswithroles_txt_mv	Cavalletti Fabio @@aut@@ Rajala Tapio @@aut@@
publishDateDaySort_date	2016-01-01T00:00:00Z
hierarchy_top_id	777285061
id	DOAJ054770149
language_de	englisch
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">DOAJ054770149</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230308184118.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230227s2016 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/agms-2016-0004</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ054770149</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA299.6-433</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Cavalletti Fabio</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Tangent Lines and Lipschitz Differentiability Spaces</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">metric geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">lipschitz differentiability spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">tangent of metric spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ricci curvature</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Analysis</subfield></datafield><datafield tag="700" ind1="0" ind2=" "><subfield code="a">Rajala Tapio</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Analysis and Geometry in Metric Spaces</subfield><subfield code="d">De Gruyter, 2015</subfield><subfield code="g">4(2016), 1</subfield><subfield code="w">(DE-627)777285061</subfield><subfield code="w">(DE-600)2753702-X</subfield><subfield code="x">22993274</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:4</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/agms-2016-0004</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/agms-2016-0004</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2299-3274</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_DOAJ</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">4</subfield><subfield code="j">2016</subfield><subfield code="e">1</subfield></datafield></record></collection>
callnumber-first	Q - Science
author	Cavalletti Fabio
spellingShingle	Cavalletti Fabio misc QA299.6-433 misc metric geometry misc lipschitz differentiability spaces misc tangent of metric spaces misc ricci curvature misc Analysis Tangent Lines and Lipschitz Differentiability Spaces
authorStr	Cavalletti Fabio
ppnlink_with_tag_str_mv	@@773@@(DE-627)777285061
format	electronic Article
delete_txt_mv	keep
author_role	aut aut
collection	DOAJ
remote_str	true
callnumber-label	QA299
illustrated	Not Illustrated
issn	22993274
topic_title	QA299.6-433 Tangent Lines and Lipschitz Differentiability Spaces metric geometry lipschitz differentiability spaces tangent of metric spaces ricci curvature
topic	misc QA299.6-433 misc metric geometry misc lipschitz differentiability spaces misc tangent of metric spaces misc ricci curvature misc Analysis
topic_unstemmed	misc QA299.6-433 misc metric geometry misc lipschitz differentiability spaces misc tangent of metric spaces misc ricci curvature misc Analysis
topic_browse	misc QA299.6-433 misc metric geometry misc lipschitz differentiability spaces misc tangent of metric spaces misc ricci curvature misc Analysis
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
format_main_str_mv	Text Zeitschrift/Artikel
carriertype_str_mv	cr
hierarchy_parent_title	Analysis and Geometry in Metric Spaces
hierarchy_parent_id	777285061
hierarchy_top_title	Analysis and Geometry in Metric Spaces
isfreeaccess_txt	true
familylinks_str_mv	(DE-627)777285061 (DE-600)2753702-X
title	Tangent Lines and Lipschitz Differentiability Spaces
ctrlnum	(DE-627)DOAJ054770149 (DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5
title_full	Tangent Lines and Lipschitz Differentiability Spaces
author_sort	Cavalletti Fabio
journal	Analysis and Geometry in Metric Spaces
journalStr	Analysis and Geometry in Metric Spaces
callnumber-first-code	Q
lang_code	eng
isOA_bool	true
recordtype	marc
publishDateSort	2016
contenttype_str_mv	txt
author_browse	Cavalletti Fabio Rajala Tapio
container_volume	4
class	QA299.6-433
format_se	Elektronische Aufsätze
author-letter	Cavalletti Fabio
doi_str_mv	10.1515/agms-2016-0004
author2-role	verfasserin
title_sort	tangent lines and lipschitz differentiability spaces
callnumber	QA299.6-433
title_auth	Tangent Lines and Lipschitz Differentiability Spaces
abstract	We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space.
abstractGer	We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space.
abstract_unstemmed	We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space.
collection_details	GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700
container_issue	1
title_short	Tangent Lines and Lipschitz Differentiability Spaces
url	https://doi.org/10.1515/agms-2016-0004 https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5 https://doaj.org/toc/2299-3274
remote_bool	true
author2	Rajala Tapio
author2Str	Rajala Tapio
ppnlink	777285061
callnumber-subject	QA - Mathematics
mediatype_str_mv	c
isOA_txt	true
hochschulschrift_bool	false
doi_str	10.1515/agms-2016-0004
callnumber-a	QA299.6-433
up_date	2024-07-04T00:31:43.228Z
_version_	1803606402782986240
fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">DOAJ054770149</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230308184118.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230227s2016 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/agms-2016-0004</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ054770149</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJ4f7d0215b35649b7804f0020319be0f5</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA299.6-433</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Cavalletti Fabio</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Tangent Lines and Lipschitz Differentiability Spaces</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves. We then show that any blow-up done at a point of metric differentiability and of density one for the domain of the curve gives a tangent line. Metric differentiability enjoys a Borel measurability property and this will permit us to use it in the framework of Lipschitz differentiability spaces.We show that any tangent space of a Lipschitz differentiability space contains at least n distinct tangent lines, obtained as the blow-up of n Lipschitz curves, where n is the dimension of the local measurable chart. Under additional assumptions on the space, such as curvature lower bounds, these n distinct tangent lines span an n-dimensional part of the tangent space.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">metric geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">lipschitz differentiability spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">tangent of metric spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ricci curvature</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Analysis</subfield></datafield><datafield tag="700" ind1="0" ind2=" "><subfield code="a">Rajala Tapio</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Analysis and Geometry in Metric Spaces</subfield><subfield code="d">De Gruyter, 2015</subfield><subfield code="g">4(2016), 1</subfield><subfield code="w">(DE-627)777285061</subfield><subfield code="w">(DE-600)2753702-X</subfield><subfield code="x">22993274</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:4</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/agms-2016-0004</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doaj.org/article/4f7d0215b35649b7804f0020319be0f5</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/agms-2016-0004</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2299-3274</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_DOAJ</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">4</subfield><subfield code="j">2016</subfield><subfield code="e">1</subfield></datafield></record></collection>
score	7.401457

Nicht das Richtige dabei?

Schreiben Sie uns!

Tangent Lines and Lipschitz Differentiability Spaces

Nicht das Richtige dabei?

Zugang & Verfügbarkeit

Vorhandene Bände

Nicht das Richtige dabei?