Calculus of Variations and Geometric Measure Theory

F. Cavalletti - F. Maggi - A. Mondino

Rigidity for critical points in the Levy-Gromov inequality

created by maggi on 13 Dec 2016
modified on 25 Apr 2018


Published Paper

Inserted: 13 dec 2016
Last Updated: 25 apr 2018

Journal: Math. Zeit
Pages: 5
Year: 2016
Doi: 10.1007/s00209-017-1993-x


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.