Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature

2022/12/09 by Davide Manini, Manini, Davide · 1 citation
Mathematics · Physics and Astronomy · #58B20 (Primary) 51Fxx (Secondary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.05130

openalex publication_date 2022/12/09 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28

Abstract

We prove a sharp isoperimetric inequality for measured Finsler manifolds having non-negative Ricci curvature and Euclidean volume growth. We also prove a rigidity result for this inequality, under the additional hypotheses of boundedness of the isoperimetric set and the finite reversibility of the space. As a consequence, we deduce the rigidity of the weighted anisotropic isoperimetric inequality for cones in the Euclidean space, in the irreversible setting.

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• Isoperimetric inequality on Finsler metric measure manifolds with non-negative weighted Ricci curvature

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