A sharp isoperimetric inequality in metric measure spaces with non-negative Ricci curvature

TL;DR

This paper establishes a precise isoperimetric inequality in non-compact metric measure spaces with non-negative Ricci curvature, linking volume entropy to geometric properties.

Contribution

It introduces a sharp, dimension-free isoperimetric inequality involving volume entropy for spaces with synthetic Ricci curvature.

Findings

Proves a sharp isoperimetric inequality in the specified spaces.

Links volume entropy to geometric inequalities.

Provides a dimension-free bound applicable to non-compact spaces.

Abstract

We prove a sharp dimension-free isoperimetric inequality, involving the volume entropy, in non-compact metric measure spaces with non-negative synthetic Ricci curvature.