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Journal Article

Width and flow of hypersurfaces by curvature functions

MPS-Authors

Calle,  Maria
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0805.1023v1.pdf
(Preprint), 209KB

TransAMS363_1125.pdf
(Any fulltext), 391KB

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Citation

Calle, M., Kleene, S. J., & Kramer, J. (2011). Width and flow of hypersurfaces by curvature functions. Transactions of the American Mathematical Society, 363(3), 1125-1135.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-6005-5
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.