English

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}
}