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Rigidity for critical points in the Lévy-Gromov inequality
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Cavalletti, Fabio, Maggi, Francesco and Mondino, Andrea (2018) Rigidity for critical points in the Lévy-Gromov inequality. Mathematische Zeitschrift, 289 (3-4). pp. 1191-1197. doi:10.1007/s00209-017-1993-x ISSN 0025-5874.
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Official URL: http://dx.doi.org/10.1007/s00209-017-1993-x
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.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Calculus of variations, Riemannian manifolds | ||||||||||||
Journal or Publication Title: | Mathematische Zeitschrift | ||||||||||||
Publisher: | Springer | ||||||||||||
ISSN: | 0025-5874 | ||||||||||||
Official Date: | August 2018 | ||||||||||||
Dates: |
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Volume: | 289 | ||||||||||||
Number: | 3-4 | ||||||||||||
Number of Pages: | 7 | ||||||||||||
Page Range: | pp. 1191-1197 | ||||||||||||
DOI: | 10.1007/s00209-017-1993-x | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 1 November 2018 | ||||||||||||
Date of first compliant Open Access: | 1 November 2018 | ||||||||||||
RIOXX Funder/Project Grant: |
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