Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds

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.

13 pages, final version to appear in Rend. Lincei Mat. Appl. arXiv admin note: text overlap with arXiv:1505.02061

Cited by in corpus (5)

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• Quantitative isoperimetry à la Levy-Gromov
• Sharp Cheeger-Buser type inequalities in $\mathsf{RCD}(K,\infty )$ spaces
• The Cheeger problem in abstract measure spaces
• A Talenti-type comparison theorem for $\mathrm{RCD}(K,N)$ spaces and applications