Open Access
October 2015 Convex ancient solutions of the mean curvature flow
Gerhard Huisken, Carlo Sinestrari
J. Differential Geom. 101(2): 267-287 (October 2015). DOI: 10.4310/jdg/1442364652


We study solutions of the mean curvature flow which are defined for all negative times, usually called ancient solutions. We give various conditions ensuring that a closed convex ancient solution is a shrinking sphere. Examples of such conditions are: a uniform pinching condition on the curvatures, a suitable growth bound on the diameter, or a reverse isoperimetric inequality. We also study the behaviour of uniformly $k$-convex solutions, and consider generalizations to ancient solutions immersed in a sphere.


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Gerhard Huisken. Carlo Sinestrari. "Convex ancient solutions of the mean curvature flow." J. Differential Geom. 101 (2) 267 - 287, October 2015.


Published: October 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1332.53085
MathSciNet: MR3399098
Digital Object Identifier: 10.4310/jdg/1442364652

Rights: Copyright © 2015 Lehigh University

Vol.101 • No. 2 • October 2015
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