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arXiv · 1405.7509

Convex ancient solutions of the mean curvature flow

G. Huisken·C. Sinestrari
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Abstract

We study solutions of the mean curvature flow which are defined for all negative curvature 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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G. Huisken, C. Sinestrari. 2014-05-29. Convex ancient solutions of the mean curvature flow. https://doi.org/10.4310/jdg%2F1442364652

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