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arXiv · 1707.01644

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

Songzi Li·Xiang-Dong Li
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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 $K\geq 0$ 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.

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Songzi Li, Xiang-Dong Li. 2017-07-06. Hamilton differential Harnack inequality and $W$-entropy for Witten Laplacian on Riemannian manifolds. https://arxiv.org/abs/1707.01644

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