Gaussian-type isoperimetric inequalities in \(\mathsf{RCD}(K,\infty)\) probability spaces for positive \(K\) (Q333009)

Summary: In this paper, we adapt the well-estabilished \(\Gamma\)-calculus techniques to the context of \(\mathsf{RCD}(K,\infty)\) spaces, proving Bobkov's local isoperimetric inequality [\textit{D. Bakry} and \textit{M. Ledoux}, Invent. Math. 123, No. 2, 259--281 (1996; Zbl 0855.58011)], [\textit{S. G. Bobkov}, Ann. Probab. 25, No. 1, 206--214 (1997; Zbl 0883.60031)] 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 \textit{G. Savaré} in [Discrete Contin. Dyn. Syst. 34, No. 4, 1641--1661 (2014; Zbl 1275.49087)].