Calculus of Variations and Geometric Measure Theory

F. Cavalletti - A. Mondino

Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds

created by mondino on 06 Mar 2017
modified on 18 Apr 2018


Accepted Paper

Inserted: 6 mar 2017
Last Updated: 18 apr 2018

Journal: Intern. Math. Res. Not.
Year: 2017


Motivated by Perelman's Pseudo Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has almost maximal volume, then in a smaller ball (in a quantified sense) it holds an almost-euclidean isoperimetric inequality.

The result is actually established in the more general framework of non-smooth spaces satisfying local Ricci curvature lower bounds in a synthetic sense via optimal transportation.