# Chow's theorem

From Diffgeom

## Statement

Let denote the 2-sphere (upto differential structure) and any Riemannian metric on . Then, the Ricci flow on starting from , becomes positive in finite time.

This, along with Hamilton's theorem on Ricci flows, gives the Ricci flow convergence theorem on compact surfaces which states that any Ricci flow starting from a Riemannian metric on a compact surface converges, at time , to a constant-curvature metric.