Rigidities of Isoperimetric inequality under nonnegative Ricci curvature
speaker: Davide Manini (SISSA Scuola Internazionale Superiore di Studi Avanzati)abstract: The sharp isoperimetric inequality for non-compact Riemannian manifolds with non-negative Ricci curvature and Euclidean volume growth has been obtained in increasing generality with different approaches in a number of contributions culminated by Balogh and Kristaly covering also m.m.s.'s verifying the non-negative Ricci curvature condition in the synthetic sense of Lott, Sturm and Villani. In sharp contrast with the compact case of positive Ricci curvature, for a large class of spaces including weighted Riemannian manifolds, no complete characterisation of the equality cases is present in the literature.
I will present a contribution in the same generality of Balogh's and Kristaly's setting. In particular I will show that the equality in the isoperimetric inequality can be attained only by metric balls. Whenever this happens the space is forced, in a measure theoretic sense, to be a cone. An application to the weighted anisotropic isoperimetric problem in Eucledean cones.
This is a joint work with Fabio Cavalletti.
timetable:
Thu 27 Oct, 17:40 - 18:05, Aula Magna Bruno Pontecorvo
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