Calculus of Variations and Geometric Measure Theory
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F. Cavalletti - F. Santarcangelo

Isoperimetric inequality under Measure-Contraction property

created by santarcangelo on 26 Oct 2018
modified by cavallett on 25 Feb 2021


Published Paper

Inserted: 26 oct 2018
Last Updated: 25 feb 2021

Journal: J. Funct. Anal.
Year: 2018


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.


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