Inserted: 10 may 2016
Last Updated: 14 sep 2016
Journal: Rend. Lincei Mat. Appl.
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.