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Extrinsic radius pinching for hypersurfaces of space forms

Julien Roth
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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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Julien Roth. 2006-03-21. Extrinsic radius pinching for hypersurfaces of space forms. https://arxiv.org/abs/math/0603494

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