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arXiv · 1701.01803

Sharp gradient estimate for heat kernels on $RCD^*(K,N)$ metric measure spaces

Jia-Cheng Huang·Hui-Chun Zhang
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Abstract

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 seem new even for smooth Riemannian manifolds.

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BibTeXRIS

Jia-Cheng Huang, Hui-Chun Zhang. 2017-01-07. Sharp gradient estimate for heat kernels on $RCD^*(K,N)$ metric measure spaces. https://arxiv.org/abs/1701.01803

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