Sharp gradient estimate for heat kernels on $RC{D}^{\ast }(K,N)$ metric measure spaces

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.

15 pages. 3 typoes corrected. arXiv admin note: text overlap with arXiv:1602.05347