English

Nonconvex ancient solutions to Curve Shortening Flow

Differential Geometry 2023-02-24 v3 Analysis of PDEs

Abstract

We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For t0t\ll0 it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle α(t)=t\alpha(t) = -t, and closed off by a small copy of the Grim Reaper translating soliton.

Keywords

Cite

@article{arxiv.2204.05253,
  title  = {Nonconvex ancient solutions to Curve Shortening Flow},
  author = {Yongzhe Zhang and Connor Olson and Ilyas Khan and Sigurd Angenent},
  journal= {arXiv preprint arXiv:2204.05253},
  year   = {2023}
}

Comments

The same result was independently obtained by Charyyev, J. in arXiv:2204.05978