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 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.

16 pages

References in corpus (1)

• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds

Cited by in corpus (2)

• Sharp Cheeger-Buser type inequalities in $\mathsf{RCD}(K,\infty )$ spaces
• The equality case in Cheeger's and Buser's inequalities on $\mathsf{RCD}$ spaces