Calculus of Variations and Geometric Measure Theory
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F. Cavalletti - F. Maggi - A. Mondino

Rigidity for critical points in the Levy-Gromov inequality

created by maggi on 13 Dec 2016



Inserted: 13 dec 2016
Last Updated: 13 dec 2016

Pages: 5
Year: 2016


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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