Width and flow of hypersurfaces by curvature functions
Differential Geometry
2008-05-08 v1
Abstract
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.
Cite
@article{arxiv.0805.1023,
title = {Width and flow of hypersurfaces by curvature functions},
author = {Maria Calle and Stephen J. Kleene and Joel Kramer},
journal= {arXiv preprint arXiv:0805.1023},
year = {2008}
}