Chow's theorem

Statement

Let $S^2$ denote the 2-sphere (upto differential structure) and $g$ any Riemannian metric on $S^2$. Then, the Ricci flow on $S^2$ starting from $g$, 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 $\mathrm{\infty }$, to a constant-curvature metric.