Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds

TL;DR

This paper extends isoperimetric inequalities and Cheeger constant results from Minkowski content to perimeter in non-branching metric measure spaces with lower Ricci curvature bounds.

Contribution

It proves that previous Minkowski content-based inequalities also hold in terms of perimeter under stronger conditions.

Findings

Isoperimetric inequalities hold in terms of perimeter.

Cheeger constant bounds are established in the new framework.

Results apply to essentially non-branching metric measure spaces.

Abstract

We prove that the results regarding the Isoperimetric inequality and Cheeger constant formulated in terms of the Minkowski content, obtained by the authors in previous papers in the framework of essentially non-branching metric measure spaces verifying the local curvature dimension condition, also hold in the stronger formulation in terms of the perimeter.