The Lévy-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 Lévy-Gromov inequality and prove that, in two-dimensions, this criticality condition is quite rigid, as it characterizes round spheres and projective planes.
Rigidity for critical points in the Lévy-Gromov inequality / F. Cavalletti, F. Maggi, A. Mondino. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 289:3-4(2018 Aug), pp. 1191-1197. [10.1007/s00209-017-1993-x]
Rigidity for critical points in the Lévy-Gromov inequality
F. CavallettiPrimo
;
2018
Abstract
The Lévy-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 Lévy-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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