Isoperimetric inequality in noncompact 𝖬𝖢𝖯 spaces

Cavalletti, Fabio; Manini, Davide

doi:10.1090/proc/15945

Isoperimetric inequality in noncompact $\mathsf {MCP}$ spaces
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by Fabio Cavalletti and Davide Manini PDF

Proc. Amer. Math. Soc. 150 (2022), 3537-3548 Request permission

Abstract:

We prove a sharp isoperimetric inequality for the class of metric measure spaces verifying the synthetic Ricci curvature lower bounds Measure Contraction property ($\mathsf {MCP}(0,N)$) and having Euclidean volume growth at infinity. We avoid the classical use of the Brunn-Minkowski inequality, not available for $\mathsf {MCP}(0,N)$, and of the PDE approach, not available in the singular setting. Our approach will be carried over by using a scaling limit of localization.

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