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Extrinsic radius pinching for hypersurfaces of space forms

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Type
Preprint
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Submission Date
Identifiers
arXiv ID: math/0603494
Source
arXiv
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Unknown
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Abstract

We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. We show that if the pinching condion is strong enough with a dependance on the norm of the second foundamental form, then the hypersurface is diffeomorphic and almost isometric to a geodesic hypersphere.

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