Sharp Logarithmic Sobolev inequalities along an extended Ricci flow and applications

Guoqiang Wu; Yu Zheng

doi:10.2140/pjm.2019.298.483

Sharp Logarithmic Sobolev inequalities along an extended Ricci flow and applications

Guoqiang Wu
, Yu Zheng

School of Mathematical Sciences

Zhejiang Sci-Tech University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove a sharp Logarithmic Sobolev inequality along an extended Ricci flow. As applications, we derive an integral bound for the conjugate heat kernel and also obtain Lipschitz continuity of the pointed Nash entropy. Finally, based on these results, we prove an ε-regularity theorem for this extended Ricci flow.

Original language	English
Pages (from-to)	483-509
Number of pages	27
Journal	Pacific Journal of Mathematics
Volume	298
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2019.298.483
State	Published - 2019

Keywords

Conjugate heat kernel
Logarithmic Sobolev inequalities
ε-regularity

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title = "Sharp Logarithmic Sobolev inequalities along an extended Ricci flow and applications",

abstract = "We prove a sharp Logarithmic Sobolev inequality along an extended Ricci flow. As applications, we derive an integral bound for the conjugate heat kernel and also obtain Lipschitz continuity of the pointed Nash entropy. Finally, based on these results, we prove an ε-regularity theorem for this extended Ricci flow.",

keywords = "Conjugate heat kernel, Logarithmic Sobolev inequalities, ε-regularity",

author = "Guoqiang Wu and Yu Zheng",

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year = "2019",

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T1 - Sharp Logarithmic Sobolev inequalities along an extended Ricci flow and applications

AU - Wu, Guoqiang

AU - Zheng, Yu

PY - 2019

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N2 - We prove a sharp Logarithmic Sobolev inequality along an extended Ricci flow. As applications, we derive an integral bound for the conjugate heat kernel and also obtain Lipschitz continuity of the pointed Nash entropy. Finally, based on these results, we prove an ε-regularity theorem for this extended Ricci flow.

AB - We prove a sharp Logarithmic Sobolev inequality along an extended Ricci flow. As applications, we derive an integral bound for the conjugate heat kernel and also obtain Lipschitz continuity of the pointed Nash entropy. Finally, based on these results, we prove an ε-regularity theorem for this extended Ricci flow.

KW - Conjugate heat kernel

KW - Logarithmic Sobolev inequalities

KW - ε-regularity

UR - https://www.scopus.com/pages/publications/85065784149

U2 - 10.2140/pjm.2019.298.483

DO - 10.2140/pjm.2019.298.483

M3 - 文章

AN - SCOPUS:85065784149

SN - 0030-8730

VL - 298

SP - 483

EP - 509

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

Sharp Logarithmic Sobolev inequalities along an extended Ricci flow and applications

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Keywords

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