Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature

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.

46 pages, a4paper. Improved according to referees' suggestions. To be published in Rev. Mat. Iberoam. arXiv admin note: text overlap with arXiv:2207.03423