Nonconvex ancient solutions to Curve Shortening Flow

Abstract

We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For $t\ll 0$ it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle $\alpha (t)=-t$, and closed off by a small copy of the Grim Reaper translating soliton.

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