Published Paper

Inserted: 9 aug 2022
Last Updated: 12 jun 2024

Journal: Mathematische Annalen
Volume: 389
Number: 2
Pages: 1677-1730
Year: 2024
Doi: 10.1007/s00208-023-02674-y

This is the second of two companion papers originally appeared in a joint version in arXiv:2201.04916v1. The first of the two companion papers is arXiv:2201.04916

Abstract:

This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on $N$-dimensional $\mathrm{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathscr{H}^N)$. Moreover, we obtain almost regularity theorems formulated in terms of the isoperimetric profile and enhanced consequences at the level of several functional inequalities. Most of our statements are new even in the classical setting of smooth, non compact manifolds with lower Ricci curvature bounds. The synthetic theory plays a key role via compactness and stability arguments.

Keywords: isoperimetric inequality, isoperimetric problem, RCD space, Lower Ricci bounds