Skip to Main content Skip to Navigation
Journal articles

Nearly round spheres look convex

Abstract : We prove that a Riemannian manifold (M, g), close enough to the round sphere in the C4 topology, has uniformly convex injectivity domains so M appears uniformly convex in any exponential chart. The proof is based on the Ma-Trudinger-Wang nonlocal curvature tensor, which originates from the regularity theory of optimal transport.
Complete list of metadatas

Cited literature [32 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00923321
Contributor : Ludovic Rifford <>
Submitted on : Thursday, January 2, 2014 - 1:41:45 PM
Last modification on : Monday, October 12, 2020 - 10:27:27 AM
Long-term archiving on: : Saturday, April 8, 2017 - 9:58:24 AM

File

FRV-Sn.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00923321, version 1

Citation

Alessio Figalli, Ludovic Rifford, Cédric Villani. Nearly round spheres look convex. American Journal of Mathematics, Johns Hopkins University Press, 2012, 134 (1), pp.109. ⟨hal-00923321⟩

Share

Metrics

Record views

651

Files downloads

363