Sharp gradient estimate for heat kernels on $RCD^*(K,N)$ metric measure spaces
Differential Geometry
2017-01-11 v2 Metric Geometry
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.
Cite
@article{arxiv.1701.01803,
title = {Sharp gradient estimate for heat kernels on $RCD^*(K,N)$ metric measure spaces},
author = {Jia-Cheng Huang and Hui-Chun Zhang},
journal= {arXiv preprint arXiv:1701.01803},
year = {2017}
}
Comments
15 pages. 3 typoes corrected. arXiv admin note: text overlap with arXiv:1602.05347