Classification of limiting shapes for isotropic curve flows-Reference-Cited by-同舟云学术

Classification of limiting shapes for isotropic curve flows

Published:2002-12-11 Issue:2 Volume:16 Page:443-459
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Andrews Ben

Abstract

A complete classification is given of curves in the plane which contract homothetically when evolved according to a power of their curvature. Applications are given to the limiting behaviour of the flows in various situations.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2003-16-02/S0894-0347-02-00415-0/S0894-0347-02-00415-0.pdf

Reference23 articles.

1. The normalized curve shortening flow and homothetic solutions;Abresch, U.;J. Differential Geom.,1986

2. Contraction of convex hypersurfaces by their affine normal;Andrews, Ben;J. Differential Geom.,1996

3. Monotone quantities and unique limits for evolving convex hypersurfaces;Andrews, Ben;Internat. Math. Res. Notices,1997

4. Evolving convex curves;Andrews, Ben;Calc. Var. Partial Differential Equations,1998

5. Motion of hypersurfaces by Gauss curvature;Andrews, Ben;Pacific J. Math.,2000

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