Pinched Ancient Solutions to the High Codimension Mean Curvature Flow
Differential Geometry
2017-09-29 v1
Abstract
We study solutions of high codimension mean curvature flow defined for all negative times, usually referred to as ancient solutions. We show that any compact ancient solution whose second fundamental form satisfies a certain natural pinching condition must be a family of shrinking spheres. Andrews and Baker have shown that initial submanifolds satisfying this pinching condition, which generalises the notion of convexity, converge to round points under the flow. As an application, we use our result to simplify their proof.
Keywords
Cite
@article{arxiv.1709.09697,
title = {Pinched Ancient Solutions to the High Codimension Mean Curvature Flow},
author = {Stephen Lynch and Huy The Nguyen},
journal= {arXiv preprint arXiv:1709.09697},
year = {2017}
}