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arXiv · 1810.11289

Isoperimetric inequality under Measure-Contraction property

Fabio Cavalletti·Flavia Santarcangelo
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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 L\'evy-Gromov holds true. Measure theoretic rigidity is also obtained.

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Fabio Cavalletti, Flavia Santarcangelo. 2018-10-26. Isoperimetric inequality under Measure-Contraction property. https://arxiv.org/abs/1810.11289

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