Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature

TL;DR

This paper establishes a sharp isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature and Euclidean volume growth, including rigidity results under specific conditions, extending to cones in Euclidean space.

Contribution

It proves a new sharp isoperimetric inequality for measured Finsler manifolds with non-negative Ricci curvature and explores rigidity under boundedness and reversibility assumptions.

Findings

Proved a sharp isoperimetric inequality for Finsler manifolds.

Established rigidity results under boundedness and reversibility.

Extended results to cones in Euclidean space in the irreversible setting.

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.