The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces

Renjin Jiang

Let $(X,d,\mu )$ be a $RC{D}^{\ast }(K,N)$ space with $K\in mathbbR$ and $N\in [1,\infty )$. Suppose that $(X,d)$ is connected, complete and separable, and $\supp μ=X$. We prove that the…