Chow's theorem

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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 \infty, to a constant-curvature metric.