Work

Nearly Round Spheres Look Convex

Year: 2012

Type: article

Abstract: We prove that a Riemannian manifold $(M,g)$, close enough to the round sphere in the $C^4$ 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.

Source: American Journal of Mathematics

DOI: 10.1353/ajm.2012.0000

Authors: A. Figalli, L. Rifford, C. Villani

Institutions: Texas Tech University, Laboratoire Jean-Alexandre Dieudonné, Institut Camille Jordan

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2081168151

FWCI: 9.772

Cites: 37

Cited by: 65

Related to: 9