Heat kernel estimates on metric measure spaces
We investigate heat kernel estimates for regular Dirichlet forms without killing terms on metric measure spaces. For a local Dirichlet from, the heat kernel admits a sub-Gaussian or a Gaussian estimate, whilst for a non-local Dirichlet from, the heat kernel admits a stable-like estimate. We will give equivalent conditions to the heat kernel estimate for both local and non-local Dirichlet forms.
This talk is based on several joint papers respectively with Alexander Grigor'yan, Eryan Hu, and Ka-Sing Lau.