Rigidity for critical points in the Levy-Gromov inequality
Differential Geometry
2020-04-22 v1 Optimization and Control
Abstract
The Levy-Gromov inequality states that round spheres have the least isoperimetric profile (normalized by total volume) among Riemannian manifolds with a fixed positive lower bound on the Ricci tensor. In this note we study critical metrics corresponding to the Levy-Gromov inequality and prove that, in two-dimensions, this criticality condition is quite rigid, as it characterizes round spheres and projective planes.
Cite
@article{arxiv.1612.04119,
title = {Rigidity for critical points in the Levy-Gromov inequality},
author = {Fabio Cavalletti and Francesco Maggi and Andrea Mondino},
journal= {arXiv preprint arXiv:1612.04119},
year = {2020}
}
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5 pages