Extrinsic Radius Pinching in Space Forms of Nonnegative Sectional Curavture
نویسنده
چکیده
We first give new estimates for the extrinsic radius of compact hypersurfaces of the Euclidean space R 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, M is diffeomorphic and almost isometric to an n-dimensional sphere.
منابع مشابه
Extrinsic Radius Pinching for Hypersurfaces of Space Forms
We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. In the hyperbolic space, we show that if the volume of M is 1, then there exists a constant C depending on the dimension of M and the L-norm of the second fundamental form B such that the pinching condition tanh(R) < 1 ||H||∞ + C (where H is the mean curvature) implies that M is diffeomorphic to an ...
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