Sharp logarithmic Sobolev inequalities along an extended Ricci flow and applications

Guoqiang Wu and Yu Zheng

Vol. 298 (2019), No. 2, 483–509

DOI: 10.2140/pjm.2019.298.483

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 $\epsilon$-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