Classification of ancient compact solutions to the ricci flow on surfaces

Abstract

We consider an ancient solution g(·, t) of the Ricci flow on a compact surface that exists for t 2 (−∞, T) and becomes spherical at time t = T. We prove that the metric g(·, t) is either a family of contracting spheres, which is a type I ancient solution, or a King-Rosenau solution, which is a type II ancient solution. © 2012 Journal of Differential Geometry. © 2012 Applied Probability Trust.