Weighted Ricci curvature in Riemann-Finsler geometry
Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry vi...
Ausführliche Beschreibung
Autor*in: |
Zhongmin Shen [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2021 |
---|
Schlagwörter: |
---|
Übergeordnetes Werk: |
In: AUT Journal of Mathematics and Computing - Amirkabir University of Technology, 2024, 2(2021), 2, Seite 117-136 |
---|---|
Übergeordnetes Werk: |
volume:2 ; year:2021 ; number:2 ; pages:117-136 |
Links: |
Link aufrufen |
---|
DOI / URN: |
10.22060/ajmc.2021.20473.1067 |
---|
Katalog-ID: |
DOAJ101631839 |
---|
LEADER | 01000naa a22002652 4500 | ||
---|---|---|---|
001 | DOAJ101631839 | ||
003 | DE-627 | ||
005 | 20240414200402.0 | ||
007 | cr uuu---uuuuu | ||
008 | 240414s2021 xx |||||o 00| ||eng c | ||
024 | 7 | |a 10.22060/ajmc.2021.20473.1067 |2 doi | |
035 | |a (DE-627)DOAJ101631839 | ||
035 | |a (DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49 | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng | ||
050 | 0 | |a QA1-939 | |
100 | 0 | |a Zhongmin Shen |e verfasserin |4 aut | |
245 | 1 | 0 | |a Weighted Ricci curvature in Riemann-Finsler geometry |
264 | 1 | |c 2021 | |
336 | |a Text |b txt |2 rdacontent | ||
337 | |a Computermedien |b c |2 rdamedia | ||
338 | |a Online-Ressource |b cr |2 rdacarrier | ||
520 | |a Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. | ||
650 | 4 | |a ricci curvature | |
650 | 4 | |a $s$-curvature | |
650 | 4 | |a mean curvature | |
653 | 0 | |a Mathematics | |
773 | 0 | 8 | |i In |t AUT Journal of Mathematics and Computing |d Amirkabir University of Technology, 2024 |g 2(2021), 2, Seite 117-136 |w (DE-627)DOAJ090664809 |x 27832287 |7 nnns |
773 | 1 | 8 | |g volume:2 |g year:2021 |g number:2 |g pages:117-136 |
856 | 4 | 0 | |u https://doi.org/10.22060/ajmc.2021.20473.1067 |z kostenfrei |
856 | 4 | 0 | |u https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49 |z kostenfrei |
856 | 4 | 0 | |u https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf |z kostenfrei |
856 | 4 | 2 | |u https://doaj.org/toc/2783-2449 |y Journal toc |z kostenfrei |
856 | 4 | 2 | |u https://doaj.org/toc/2783-2287 |y Journal toc |z kostenfrei |
912 | |a GBV_USEFLAG_A | ||
912 | |a SYSFLAG_A | ||
912 | |a GBV_DOAJ | ||
951 | |a AR | ||
952 | |d 2 |j 2021 |e 2 |h 117-136 |
author_variant |
z s zs |
---|---|
matchkey_str |
article:27832287:2021----::egtdiccrauenimnf |
hierarchy_sort_str |
2021 |
callnumber-subject-code |
QA |
publishDate |
2021 |
allfields |
10.22060/ajmc.2021.20473.1067 doi (DE-627)DOAJ101631839 (DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49 DE-627 ger DE-627 rakwb eng QA1-939 Zhongmin Shen verfasserin aut Weighted Ricci curvature in Riemann-Finsler geometry 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. ricci curvature $s$-curvature mean curvature Mathematics In AUT Journal of Mathematics and Computing Amirkabir University of Technology, 2024 2(2021), 2, Seite 117-136 (DE-627)DOAJ090664809 27832287 nnns volume:2 year:2021 number:2 pages:117-136 https://doi.org/10.22060/ajmc.2021.20473.1067 kostenfrei https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49 kostenfrei https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf kostenfrei https://doaj.org/toc/2783-2449 Journal toc kostenfrei https://doaj.org/toc/2783-2287 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 2 2021 2 117-136 |
spelling |
10.22060/ajmc.2021.20473.1067 doi (DE-627)DOAJ101631839 (DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49 DE-627 ger DE-627 rakwb eng QA1-939 Zhongmin Shen verfasserin aut Weighted Ricci curvature in Riemann-Finsler geometry 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. ricci curvature $s$-curvature mean curvature Mathematics In AUT Journal of Mathematics and Computing Amirkabir University of Technology, 2024 2(2021), 2, Seite 117-136 (DE-627)DOAJ090664809 27832287 nnns volume:2 year:2021 number:2 pages:117-136 https://doi.org/10.22060/ajmc.2021.20473.1067 kostenfrei https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49 kostenfrei https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf kostenfrei https://doaj.org/toc/2783-2449 Journal toc kostenfrei https://doaj.org/toc/2783-2287 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 2 2021 2 117-136 |
allfields_unstemmed |
10.22060/ajmc.2021.20473.1067 doi (DE-627)DOAJ101631839 (DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49 DE-627 ger DE-627 rakwb eng QA1-939 Zhongmin Shen verfasserin aut Weighted Ricci curvature in Riemann-Finsler geometry 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. ricci curvature $s$-curvature mean curvature Mathematics In AUT Journal of Mathematics and Computing Amirkabir University of Technology, 2024 2(2021), 2, Seite 117-136 (DE-627)DOAJ090664809 27832287 nnns volume:2 year:2021 number:2 pages:117-136 https://doi.org/10.22060/ajmc.2021.20473.1067 kostenfrei https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49 kostenfrei https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf kostenfrei https://doaj.org/toc/2783-2449 Journal toc kostenfrei https://doaj.org/toc/2783-2287 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 2 2021 2 117-136 |
allfieldsGer |
10.22060/ajmc.2021.20473.1067 doi (DE-627)DOAJ101631839 (DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49 DE-627 ger DE-627 rakwb eng QA1-939 Zhongmin Shen verfasserin aut Weighted Ricci curvature in Riemann-Finsler geometry 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. ricci curvature $s$-curvature mean curvature Mathematics In AUT Journal of Mathematics and Computing Amirkabir University of Technology, 2024 2(2021), 2, Seite 117-136 (DE-627)DOAJ090664809 27832287 nnns volume:2 year:2021 number:2 pages:117-136 https://doi.org/10.22060/ajmc.2021.20473.1067 kostenfrei https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49 kostenfrei https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf kostenfrei https://doaj.org/toc/2783-2449 Journal toc kostenfrei https://doaj.org/toc/2783-2287 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 2 2021 2 117-136 |
allfieldsSound |
10.22060/ajmc.2021.20473.1067 doi (DE-627)DOAJ101631839 (DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49 DE-627 ger DE-627 rakwb eng QA1-939 Zhongmin Shen verfasserin aut Weighted Ricci curvature in Riemann-Finsler geometry 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. ricci curvature $s$-curvature mean curvature Mathematics In AUT Journal of Mathematics and Computing Amirkabir University of Technology, 2024 2(2021), 2, Seite 117-136 (DE-627)DOAJ090664809 27832287 nnns volume:2 year:2021 number:2 pages:117-136 https://doi.org/10.22060/ajmc.2021.20473.1067 kostenfrei https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49 kostenfrei https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf kostenfrei https://doaj.org/toc/2783-2449 Journal toc kostenfrei https://doaj.org/toc/2783-2287 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 2 2021 2 117-136 |
language |
English |
source |
In AUT Journal of Mathematics and Computing 2(2021), 2, Seite 117-136 volume:2 year:2021 number:2 pages:117-136 |
sourceStr |
In AUT Journal of Mathematics and Computing 2(2021), 2, Seite 117-136 volume:2 year:2021 number:2 pages:117-136 |
format_phy_str_mv |
Article |
institution |
findex.gbv.de |
topic_facet |
ricci curvature $s$-curvature mean curvature Mathematics |
isfreeaccess_bool |
true |
container_title |
AUT Journal of Mathematics and Computing |
authorswithroles_txt_mv |
Zhongmin Shen @@aut@@ |
publishDateDaySort_date |
2021-01-01T00:00:00Z |
hierarchy_top_id |
DOAJ090664809 |
id |
DOAJ101631839 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">DOAJ101631839</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240414200402.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240414s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.22060/ajmc.2021.20473.1067</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ101631839</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49</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">QA1-939</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Zhongmin Shen</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Weighted Ricci curvature in Riemann-Finsler geometry</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</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">Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ricci curvature</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">$s$-curvature</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">mean curvature</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">AUT Journal of Mathematics and Computing</subfield><subfield code="d">Amirkabir University of Technology, 2024</subfield><subfield code="g">2(2021), 2, Seite 117-136</subfield><subfield code="w">(DE-627)DOAJ090664809</subfield><subfield code="x">27832287</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:2</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:2</subfield><subfield code="g">pages:117-136</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.22060/ajmc.2021.20473.1067</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2783-2449</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2783-2287</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="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">2</subfield><subfield code="j">2021</subfield><subfield code="e">2</subfield><subfield code="h">117-136</subfield></datafield></record></collection>
|
callnumber-first |
Q - Science |
author |
Zhongmin Shen |
spellingShingle |
Zhongmin Shen misc QA1-939 misc ricci curvature misc $s$-curvature misc mean curvature misc Mathematics Weighted Ricci curvature in Riemann-Finsler geometry |
authorStr |
Zhongmin Shen |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)DOAJ090664809 |
format |
electronic Article |
delete_txt_mv |
keep |
author_role |
aut |
collection |
DOAJ |
remote_str |
true |
callnumber-label |
QA1-939 |
illustrated |
Not Illustrated |
issn |
27832287 |
topic_title |
QA1-939 Weighted Ricci curvature in Riemann-Finsler geometry ricci curvature $s$-curvature mean curvature |
topic |
misc QA1-939 misc ricci curvature misc $s$-curvature misc mean curvature misc Mathematics |
topic_unstemmed |
misc QA1-939 misc ricci curvature misc $s$-curvature misc mean curvature misc Mathematics |
topic_browse |
misc QA1-939 misc ricci curvature misc $s$-curvature misc mean curvature misc Mathematics |
format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
cr |
hierarchy_parent_title |
AUT Journal of Mathematics and Computing |
hierarchy_parent_id |
DOAJ090664809 |
hierarchy_top_title |
AUT Journal of Mathematics and Computing |
isfreeaccess_txt |
true |
familylinks_str_mv |
(DE-627)DOAJ090664809 |
title |
Weighted Ricci curvature in Riemann-Finsler geometry |
ctrlnum |
(DE-627)DOAJ101631839 (DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49 |
title_full |
Weighted Ricci curvature in Riemann-Finsler geometry |
author_sort |
Zhongmin Shen |
journal |
AUT Journal of Mathematics and Computing |
journalStr |
AUT Journal of Mathematics and Computing |
callnumber-first-code |
Q |
lang_code |
eng |
isOA_bool |
true |
recordtype |
marc |
publishDateSort |
2021 |
contenttype_str_mv |
txt |
container_start_page |
117 |
author_browse |
Zhongmin Shen |
container_volume |
2 |
class |
QA1-939 |
format_se |
Elektronische Aufsätze |
author-letter |
Zhongmin Shen |
doi_str_mv |
10.22060/ajmc.2021.20473.1067 |
title_sort |
weighted ricci curvature in riemann-finsler geometry |
callnumber |
QA1-939 |
title_auth |
Weighted Ricci curvature in Riemann-Finsler geometry |
abstract |
Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. |
abstractGer |
Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. |
abstract_unstemmed |
Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds. |
collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ |
container_issue |
2 |
title_short |
Weighted Ricci curvature in Riemann-Finsler geometry |
url |
https://doi.org/10.22060/ajmc.2021.20473.1067 https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49 https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf https://doaj.org/toc/2783-2449 https://doaj.org/toc/2783-2287 |
remote_bool |
true |
ppnlink |
DOAJ090664809 |
callnumber-subject |
QA - Mathematics |
mediatype_str_mv |
c |
isOA_txt |
true |
hochschulschrift_bool |
false |
doi_str |
10.22060/ajmc.2021.20473.1067 |
callnumber-a |
QA1-939 |
up_date |
2024-07-03T21:41:12.193Z |
_version_ |
1803595674754744320 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">DOAJ101631839</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240414200402.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240414s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.22060/ajmc.2021.20473.1067</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ101631839</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJcbfd8b9e1ae04891b8888cfc42416b49</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">QA1-939</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Zhongmin Shen</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Weighted Ricci curvature in Riemann-Finsler geometry</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</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">Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic fields. Then one can estimate the Laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ricci curvature</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">$s$-curvature</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">mean curvature</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">AUT Journal of Mathematics and Computing</subfield><subfield code="d">Amirkabir University of Technology, 2024</subfield><subfield code="g">2(2021), 2, Seite 117-136</subfield><subfield code="w">(DE-627)DOAJ090664809</subfield><subfield code="x">27832287</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:2</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:2</subfield><subfield code="g">pages:117-136</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.22060/ajmc.2021.20473.1067</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doaj.org/article/cbfd8b9e1ae04891b8888cfc42416b49</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2783-2449</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2783-2287</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="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">2</subfield><subfield code="j">2021</subfield><subfield code="e">2</subfield><subfield code="h">117-136</subfield></datafield></record></collection>
|
score |
7.3987684 |