# Convex ancient solutions of the mean curvature flow

@article{Huisken2014ConvexAS,
title={Convex ancient solutions of the mean curvature flow},
author={Gerhard Huisken and Carlo Sinestrari},
journal={Journal of Differential Geometry},
year={2014},
volume={101},
pages={267-287}
}
• Published 29 May 2014
• Mathematics
• Journal of Differential Geometry
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…

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