Hamilton differential Harnack inequality and $W$-entropy for Witten Laplacian on Riemannian manifolds

Abstract

In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the $CD(-K,m)$-condition, where $m\in [n,\infty )$ and $K\ge 0$ are two constants. Moreover, we introduce the $W$-entropy and prove the $W$-entropy formula for the fundamental solution of the Witten Laplacian on complete Riemannian manifolds with the $CD(-K,m)$-condition and on compact manifolds equipped with $(-K,m)$-super Ricci flows.

To appear in Journal of Functional Analysis. This paper is an improved version of a part of our previous preprint [14] (arxiv:1412.7034, version1 (22 December 2014) and version 2 (7 February 2016))

References in corpus (1)

• On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows

Cited by in corpus (1)

• $W$-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds