Extrinsic radius pinching in space forms of nonnegative sectional curvature

Abstract : We give new estimates for the extrinsic radius of compact hypersurfaces of the Euclidean space and the open hemisphere in terms of high order mean curvatures. Then we prove pinching results corresponding to theses estimates. We show that under a suitable pinching condition, the hypersurface is diffeomorphic and almost isometric to a geodesic hypersphere.
Document type :
Journal articles
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00095786
Contributor : Julien Roth <>
Submitted on : Monday, September 18, 2006 - 1:30:44 PM
Last modification on : Monday, October 29, 2018 - 3:30:04 PM
Long-term archiving on : Tuesday, April 6, 2010 - 1:01:00 AM

Identifiers

Collections

Citation

Julien Roth. Extrinsic radius pinching in space forms of nonnegative sectional curvature. Mathematische Zeitschrift, Springer, 2008, 258 (1), pp.227-240. ⟨hal-00095786⟩

Share

Metrics

Record views

200

Files downloads

301