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

In this paper we adapt the well-estabilished $\mathrm{\Gamma }$-calculus techniques to the context of $RCD(K,\mathrm{\infty })$ 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 ${\mathrm{\Gamma }}_2$ operator introduced by Savar'e.