Width and flow of hypersurfaces by curvature functions

Details Width and flow of hypersurfaces by curvature functions Width and flow of hypersurfaces by curvature functions

2008-05-07

arxiv.org/abs/0805.1023v1

Mathematics

Differential Geometry

Scientific paper

We give a bound on the extinction time for a compact, strictly convex hypersurface in R^{n+1} evolving by a geometric flow where the velocity is given in terms of the curvature. This result generalizes a theorem of Colding and Minicozzi for mean curvature flow solutions to a wider class of flows studied by Ben Andrews. In the proof, we use the concept of the width of a hypersurface, introduced by Colding and Minicozzi. We also extend the result to 2-convex hypersurfaces, using the 2-width.

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