%0 Journal Article
%T The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces
%A Renjin Jiang
%J Mathematics
%D 2014
%I arXiv
%X Let $(X,d,\mu)$ be a $RCD^\ast(K, N)$ space with $K\in mathbb{R}$ and $N\in [1,\infty)$. Suppose that $(X,d)$ is connected, complete and separable, and $\supp \mu=X$. We prove that the Li-Yau inequality for the heat flow holds true on $(X,d,\mu)$ when $K\ge 0$. A Baudoin-Garofalo inequality and Harnack inequalities for the heat flows are established on $(X,d,\mu)$ for general $K\in \mathbb{R}$. Large time behaviors of heat kernels are also studied.
%U http://arxiv.org/abs/1405.0684v2