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

10aIsoperimetric inequality10aMeasure-Contraction property10aOptimal transport10aRicci curvature1 aCavalletti, Fabio1 aSantarcangelo, Flavia uhttps://www.sciencedirect.com/science/article/pii/S0022123619302289