# Isoperimetric inequality under Measure-Contraction property

created by santarcangelo on 26 Oct 2018

[BibTeX]

Preprint

Inserted: 26 oct 2018
Last Updated: 26 oct 2018

Year: 2018

Abstract:

We prove that if $(X,\mathsf d,\mathfrak m)$ is an essentially non-branching metric measure space with $\mathfrak m(X)=1$, having Ricci curvature bounded from below by $K$ and dimension bounded from above by $N \in (1,\infty)$, understood as a synthetic condition called Measure-Contraction property, then a sharp isoperimetric inequality a la Levy-Gromov holds true. Measure theoretic rigidity is also obtained.