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.

%V 277 %P 2893 - 2917 %8 2019/11/01/ %@ 0022-1236 %G eng %U https://www.sciencedirect.com/science/article/pii/S0022123619302289 %N 9 %! Journal of Functional Analysis