paper

Isoperimetric inequality in noncompact MCP spaces

arXiv:2110.07528

Abstract

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

11 pages; proof of main inequality and theorem 3.2 corrected; minor typos corrected