Gaussian-type isoperimetric inequalities in RCD $(K,\infty )$ probability spaces for positive $K$

Abstract

In this paper we adapt the well-estabilished $\Gamma$-calculus techniques to the context of RCD $(K,\infty )$ spaces, proving Bobkov’s local isoperimetric inequality [12], [13] and, when $K$ is positive, the Gaussian isoperimetric inequality in this class of spaces. The proof relies on the measure-valued ${\Gamma }_2$ operator introduced by Savaré in [22].