Classification of compact ancient solutions to the Ricci flow on surfaces

Details Classification of compact ancient solutions to the Ricci flow on surfaces Classification of compact ancient solutions to the Ricci flow on surfaces

2009-02-06

arxiv.org/abs/0902.1158v2

Mathematics

Differential Geometry

Scientific paper

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.

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