Convex ancient solutions of the mean curvature flow
Differential Geometry
2018-05-23 v1
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.
Keywords
Cite
@article{arxiv.1405.7509,
title = {Convex ancient solutions of the mean curvature flow},
author = {G. Huisken and C. Sinestrari},
journal= {arXiv preprint arXiv:1405.7509},
year = {2018}
}