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arXiv · 1612.04119

Rigidity for critical points in the Levy-Gromov inequality

Fabio Cavalletti·Francesco Maggi·Andrea Mondino
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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.

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Fabio Cavalletti, Francesco Maggi, Andrea Mondino. 2016-12-13. Rigidity for critical points in the Levy-Gromov inequality. https://doi.org/10.1007/s00209-017-1993-x

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