Characterizing Classical Minimal Surfaces Via the Entropy Differential

Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a con...
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Autor*in:	Bernstein, Jacob [verfasserIn] Mettler, Thomas

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	Minimal surfaces Conservation laws Schwarzian derivative

Anmerkung:	© Mathematica Josephina, Inc. 2017

Übergeordnetes Werk:	Enthalten in: The journal of geometric analysis - New York, NY : Springer, 1991, 27(2017), 3 vom: 24. Jan., Seite 2235-2268
Übergeordnetes Werk:	volume:27 ; year:2017 ; number:3 ; day:24 ; month:01 ; pages:2235-2268

Links:	Volltext

DOI / URN:	10.1007/s12220-017-9759-6

Katalog-ID:	SPR025409441

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520			\|a Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem.
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publishDate	2017
allfields	10.1007/s12220-017-9759-6 doi (DE-627)SPR025409441 (SPR)s12220-017-9759-6-e DE-627 ger DE-627 rakwb eng Bernstein, Jacob verfasserin aut Characterizing Classical Minimal Surfaces Via the Entropy Differential 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2017 Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem. Minimal surfaces (dpeaa)DE-He213 Conservation laws (dpeaa)DE-He213 Schwarzian derivative (dpeaa)DE-He213 Mettler, Thomas (orcid)0000-0002-9129-9495 aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 27(2017), 3 vom: 24. Jan., Seite 2235-2268 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:27 year:2017 number:3 day:24 month:01 pages:2235-2268 https://dx.doi.org/10.1007/s12220-017-9759-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2017 3 24 01 2235-2268
spelling	10.1007/s12220-017-9759-6 doi (DE-627)SPR025409441 (SPR)s12220-017-9759-6-e DE-627 ger DE-627 rakwb eng Bernstein, Jacob verfasserin aut Characterizing Classical Minimal Surfaces Via the Entropy Differential 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2017 Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem. Minimal surfaces (dpeaa)DE-He213 Conservation laws (dpeaa)DE-He213 Schwarzian derivative (dpeaa)DE-He213 Mettler, Thomas (orcid)0000-0002-9129-9495 aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 27(2017), 3 vom: 24. Jan., Seite 2235-2268 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:27 year:2017 number:3 day:24 month:01 pages:2235-2268 https://dx.doi.org/10.1007/s12220-017-9759-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2017 3 24 01 2235-2268
allfields_unstemmed	10.1007/s12220-017-9759-6 doi (DE-627)SPR025409441 (SPR)s12220-017-9759-6-e DE-627 ger DE-627 rakwb eng Bernstein, Jacob verfasserin aut Characterizing Classical Minimal Surfaces Via the Entropy Differential 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2017 Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem. Minimal surfaces (dpeaa)DE-He213 Conservation laws (dpeaa)DE-He213 Schwarzian derivative (dpeaa)DE-He213 Mettler, Thomas (orcid)0000-0002-9129-9495 aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 27(2017), 3 vom: 24. Jan., Seite 2235-2268 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:27 year:2017 number:3 day:24 month:01 pages:2235-2268 https://dx.doi.org/10.1007/s12220-017-9759-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2017 3 24 01 2235-2268
allfieldsGer	10.1007/s12220-017-9759-6 doi (DE-627)SPR025409441 (SPR)s12220-017-9759-6-e DE-627 ger DE-627 rakwb eng Bernstein, Jacob verfasserin aut Characterizing Classical Minimal Surfaces Via the Entropy Differential 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2017 Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem. Minimal surfaces (dpeaa)DE-He213 Conservation laws (dpeaa)DE-He213 Schwarzian derivative (dpeaa)DE-He213 Mettler, Thomas (orcid)0000-0002-9129-9495 aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 27(2017), 3 vom: 24. Jan., Seite 2235-2268 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:27 year:2017 number:3 day:24 month:01 pages:2235-2268 https://dx.doi.org/10.1007/s12220-017-9759-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2017 3 24 01 2235-2268
allfieldsSound	10.1007/s12220-017-9759-6 doi (DE-627)SPR025409441 (SPR)s12220-017-9759-6-e DE-627 ger DE-627 rakwb eng Bernstein, Jacob verfasserin aut Characterizing Classical Minimal Surfaces Via the Entropy Differential 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Mathematica Josephina, Inc. 2017 Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem. Minimal surfaces (dpeaa)DE-He213 Conservation laws (dpeaa)DE-He213 Schwarzian derivative (dpeaa)DE-He213 Mettler, Thomas (orcid)0000-0002-9129-9495 aut Enthalten in The journal of geometric analysis New York, NY : Springer, 1991 27(2017), 3 vom: 24. Jan., Seite 2235-2268 (DE-627)496971867 (DE-600)2199635-0 1559-002X nnns volume:27 year:2017 number:3 day:24 month:01 pages:2235-2268 https://dx.doi.org/10.1007/s12220-017-9759-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2017 3 24 01 2235-2268
language	English
source	Enthalten in The journal of geometric analysis 27(2017), 3 vom: 24. Jan., Seite 2235-2268 volume:27 year:2017 number:3 day:24 month:01 pages:2235-2268
sourceStr	Enthalten in The journal of geometric analysis 27(2017), 3 vom: 24. Jan., Seite 2235-2268 volume:27 year:2017 number:3 day:24 month:01 pages:2235-2268
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Minimal surfaces Conservation laws Schwarzian derivative
isfreeaccess_bool	false
container_title	The journal of geometric analysis
authorswithroles_txt_mv	Bernstein, Jacob @@aut@@ Mettler, Thomas @@aut@@
publishDateDaySort_date	2017-01-24T00:00:00Z
hierarchy_top_id	496971867
id	SPR025409441
language_de	englisch
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author	Bernstein, Jacob
spellingShingle	Bernstein, Jacob misc Minimal surfaces misc Conservation laws misc Schwarzian derivative Characterizing Classical Minimal Surfaces Via the Entropy Differential
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topic_title	Characterizing Classical Minimal Surfaces Via the Entropy Differential Minimal surfaces (dpeaa)DE-He213 Conservation laws (dpeaa)DE-He213 Schwarzian derivative (dpeaa)DE-He213
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title	Characterizing Classical Minimal Surfaces Via the Entropy Differential
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title_full	Characterizing Classical Minimal Surfaces Via the Entropy Differential
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title_sort	characterizing classical minimal surfaces via the entropy differential
title_auth	Characterizing Classical Minimal Surfaces Via the Entropy Differential
abstract	Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem. © Mathematica Josephina, Inc. 2017
abstractGer	Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem. © Mathematica Josephina, Inc. 2017
abstract_unstemmed	Abstract We introduce on any smooth oriented minimal surface in Euclidean 3-space a meromorphic quadratic differential, P, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natural geometric functional—which is, essentially, the entropy of the Gauss curvature. We characterize several classical surfaces—including Enneper’s surface, the catenoid, and the helicoid—in terms of P. As an application, we prove a novel curvature estimate for embedded minimal surfaces with small entropy differential and an associated compactness theorem. © Mathematica Josephina, Inc. 2017
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title_short	Characterizing Classical Minimal Surfaces Via the Entropy Differential
url	https://dx.doi.org/10.1007/s12220-017-9759-6
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Characterizing Classical Minimal Surfaces Via the Entropy Differential

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