Poisson Equation and Isoperimetric inequality on metric spaces

Renjin Jiang

Abstract:
In this talk, we will talk about ioperimetric inequality and regularity of
solutions to Poisson equation on metric spaces. Given a metric spaces
$(X,d)$ equipped with a locally Ahlfors measure $\mu$, we show that
solutions to Poisson equation enjoy Euclidean type property, provided
a local 2-Poincar\'e inequality and a suitable curvature condition hold.
As a result, the regularity of solutions yields a Euclidean type
isoperimetric inequality.