Xiang-Dong Li
Published 2013-03-06, updated 2014-11-06Version 4
In this paper, we prove Hamilton's Harnack inequality and the gradient estimates of the logarithmic heat kernel for the Witten Laplacian on complete Riemainnian 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.
Comments: An improved version of Hamilton's Harnack inequality is given. The Introduction part and Section 2 have been revised. Section 8 is removed
Classical large deviations theorems on complete Riemannian manifolds
Transportation on spheres via an entropy formula
On the $L^p$-estimates for Beurling-Ahlfors and Riesz transforms on Riemannian manifolds
![QR code for arXiv:1303.1242 [math.PR]](http://oss.arxitics.com/images/favicon.svg)