Calculus of Variations and Geometric Measure Theory

L. Ambrosio - A. Mondino

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

created by ambrosio on 10 May 2016
modified by mondino on 14 Sep 2016


Published Paper

Inserted: 10 may 2016
Last Updated: 14 sep 2016

Journal: Rend. Lincei Mat. Appl.
Volume: 27
Pages: 497–514
Year: 2016
Doi: DOI 10.4171/RLM/745


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 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 Savar\'e.