Vol. 298, No. 2, 2019

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Sharp logarithmic Sobolev inequalities along an extended Ricci flow and applications

Guoqiang Wu and Yu Zheng

Vol. 298 (2019), No. 2, 483–509
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, $\varepsilon$-regularity.
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 53C21
Milestones
Received: 20 January 2018
Revised: 15 May 2018
Accepted: 24 June 2018
Published: 8 March 2019
Authors
Guoqiang Wu
School of Science
Zhejiang Sci-Tech University
Hangzhou
China
Yu Zheng
School of Mathematical Sciences
East China Normal University
Shanghai
China