Classification of compact ancient solutions to the Ricci flow on surfaces

Abstract

We consider an ancient solution $g(\cdot ,t)$ of the Ricci flow on a compact surface that exists for $t\in (-\infty ,T)$ and becomes spherical at time $t=T$. We prove that the metric $g(\cdot ,t)$ is either a family of contracting spheres, which is a type I ancient solution, or a Rosenau solution, which is a type II ancient solution.

References in corpus (1)

• Classification of compact ancient solutions to the curve shortening flow

Cited by in corpus (5)

• Black Ripples, Flowers and Dumbbells at large $D$
• Ancient solutions of Ricci flow on spheres and generalized Hopf fibrations
• On the Hamilton's isoperimetric ratio in complete Riemannian manifolds of finite volume
• Ancient solutions for Andrews' hypersurface flow
• A pseudolocality theorem for Ricci flow