Uniqueness of convex ancient solutions to hypersurface flows
Differential Geometry
2021-03-04 v1
Abstract
We show that every convex ancient solution of mean curvature flow with Type I curvature growth is either spherical, cylindrical, or planar. We then prove the corresponding statement for flows by a natural class of curvature functions which are convex or concave in the second fundamental form. Neither of these results assumes interior noncollapsing.
Keywords
Cite
@article{arxiv.2103.02314,
title = {Uniqueness of convex ancient solutions to hypersurface flows},
author = {Stephen Lynch},
journal= {arXiv preprint arXiv:2103.02314},
year = {2021}
}