Sharp gradient estimate for heat kernels on   metric measure spaces with Ricci curvatuer bounded below

HUANG Jiacheng; ZHANG Huichun

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Sharp gradient estimate for heat kernels on metric measure spaces with Ricci curvatuer bounded below

HUANG Jiacheng 1,ZHANG Huichun 2 * #

1.School of Mathematical Sciences, Fudan University, Shanghai 200433

2.Department of Mathematis, Sun Yat-sen University, Guangzhou, 510275

*Correspondence author

#Submitted by

Subject:

Funding: NSFC（No.11521101）

Opened online:24 October 2016

Accepted by: none

Citation: HUANG Jiacheng,ZHANG Huichun.Sharp gradient estimate for heat kernels on metric measure spaces with Ricci curvatuer bounded below[OL]. [24 October 2016] http://en.paper.edu.cn/en_releasepaper/content/4707092

In this paper, we will establish an elliptic local Li-Yau gradient estimate for weak solutions of the heat equation on metric measure spaces with generalized Ricci curvature bounded from below. One of its main applications is a sharp gradient estimate for the logarithm of heat kernels. These results are new even for smooth Riemannian manifolds.

Keywords:Metric measure space, Ricci curvature, heat kernel, gradient estimate.

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