Pinching estimates and motion of hypersurfaces by curvature functions

Details Pinching estimates and motion of hypersurfaces by curvature functions Pinching estimates and motion of hypersurfaces by curvature functions

2004-02-19

arxiv.org/abs/math/0402311v1

Mathematics

Differential Geometry

16 pages

Scientific paper

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 analysis of gradient terms in the equations satisfied by second derivatives.

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