General Sobolev--Poincaré type Inequalities and applications to heat kernel estimates
In this talk, I discuss how a Poincaré inequality with respect to a fixed doubling measure can be used to establish Sobolev--Poincaré type inequalities for general Radon measures. This approach provides tools to analyze general energies on metric spaces, including non-linear or non-local energies, and also their connections to general Radon measures. I will also present some applications to heat kernel estimates.
This talk is based on the preprint arXiv:2509.04155