Work

Explicit rigidity of almost-umbilical hypersurfaces

Year: 2018

Type: article

Abstract: We give an explicit estimate of the distance of a closed, connected, oriented and immersed hypersurface of a space form to a geodesic sphere and show that the spherical closeness can be controlled by a power of an integral norm of the traceless second fundamental form, whenever the latter is sufficiently small. Furthermore we use the inverse mean curvature flow in the hyperbolic space to deduce the best possible order of decay in the class of C∞-bounded hypersurfaces of the Euclidean space. Keywords pinching, almost-umbilical hypersurfaces, inverse mean curvature flow

Source: Asian Journal of Mathematics

DOI: 10.4310/ajm.2018.v22.n6.a5

Authors: Julien Roth, Julian Scheuer

Institutions: Centre National de la Recherche Scientifique, Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées, University of Freiburg

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2271901032

FWCI: 1.39

Cites: 18

Cited by: 8

Related to: 10