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 $\epsilon$-regularity theorem for this extended Ricci flow.

Keywords
conjugate heat kernel, logarithmic Sobolev inequalities, $\varepsilon$-regularity.
Primary: 53C44
Secondary: 53C21