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 ≪ 0 t\ll 0 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.