Hamilton’s Harnack inequality and the W-entropy formula on complete Riemannian manifolds

Xiang-Dong Li

Stochastic Processes and their Applications, 2016, vol. 126, issue 4, 1264-1283

Abstract: In this paper, we prove Hamilton’s Harnack inequality and the gradient estimates of the logarithmic heat kernel for the Witten Laplacian on complete Riemannian manifolds. As applications, we prove the W-entropy formula for the Witten Laplacian on complete Riemannian manifolds, and prove a family of logarithmic Sobolev inequalities on complete Riemannian manifolds with natural geometric condition.

Keywords: Hamilton’s Harnack inequality; Gradient estimates; Logarithmic heat kernel; Witten Laplacian; W-entropy formula (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2015.11.002

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