Journal of Differential Geometry

Convex ancient solutions of the mean curvature flow

Gerhard Huisken and Carlo Sinestrari

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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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J. Differential Geom., Volume 101, Number 2 (2015), 267-287.

First available in Project Euclid: 16 September 2015

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Huisken, Gerhard; Sinestrari, Carlo. Convex ancient solutions of the mean curvature flow. J. Differential Geom. 101 (2015), no. 2, 267--287. doi:10.4310/jdg/1442364652.

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