Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

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 $(X,\mathsf{d},{\mathcal{H}}^N)$. 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.

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

References in corpus (4)

• Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds
• On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
• Isoperimetric sets in spaces with lower bounds on the Ricci curvature
• The isoperimetric problem via direct method in noncompact metric measure spaces with lower Ricci bounds

Cited by in corpus (7)

• Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds
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• Optimal Transport Approach to Michael-Simon-Sobolev Inequalities in Manifolds with Intermediate Ricci Curvature Lower Bounds
• Principal frequency of clamped plates on RCD(0,N) spaces: sharpness, rigidity and stability
• From bubbles to clusters: Multiple solutions to the Allen--Cahn system