Classification of compact ancient solutions to the curve shortening flow

Abstract

We consider an embedded convex compact ancient solution Гt to the curve shortening flow in ℝ2. We prove that Гt is either a family of contracting circles, which is a type I ancient solution, or a family of evolving Angenent ovals, which is of type II. © 2010 Journal of Differential Geometry. © 2010 Applied Probability Trust.