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

Luigi Ambrosio; Andrea Mondino

doi:10.4171/rlm/745

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arXiv · 1605.02852

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

Luigi Ambrosio·Andrea Mondino

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Abstract

In this paper we adapt the well-estabilished $Γ$-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 $Γ_2$ operator introduced by Savaré.

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BibTeX RIS

Luigi Ambrosio, Andrea Mondino. 2016-05-10. Gaussian-type Isoperimetric Inequalities in $RCD(K,\infty)$ probability spaces for positive $K$. https://doi.org/10.4171/rlm%2F745

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