New Pinching Estimates for Inverse Curvature Flows in Space Forms
نویسندگان
چکیده
منابع مشابه
Pinching Estimates and Motion of Hypersurfaces by Curvature Functions
Second derivative pinching estimates are proved for a class of elliptic and parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply convergence of convex hypersurfaces to spheres under these flows, improving earlier results of B. Chow and the author. The result is obtained via a detailed ...
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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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In this paper we shall discuss hypersurfaces M of space forms of constant curvature; where curvature means one of the symmetric functions of curvature associated to the second fundamental form. The values of the constant will be chosen so that the linearized equation will be an elliptic equation onM . For example, for surfaces in 3 the two possible curvatures are the mean curvature H and the Ga...
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ژورنال
عنوان ژورنال: The Journal of Geometric Analysis
سال: 2018
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-018-0051-1