Ancient solutions of the mean curvature flow
Differential Geometry
2013-08-20 v1
Abstract
In this short article, we prove the existence of ancient solutions of the mean curvature flow that for t -> 0 collapse to a round point, but for t -> -infinity become more and more oval: near the center they have asymptotic shrinkers modeled on round cylinders S^j x R^n-j and near the tips they have asymptotic translators modeled on Bowl^j+1 x R^n-j-1. We also give a characterization of the round shrinking sphere among ancient alpha-Andrews flows. Our proofs are based on the recent estimates of Haslhofer-Kleiner.
Keywords
Cite
@article{arxiv.1308.4095,
title = {Ancient solutions of the mean curvature flow},
author = {Robert Haslhofer and Or Hershkovits},
journal= {arXiv preprint arXiv:1308.4095},
year = {2013}
}
Comments
9 pages