In differential geometry, Ricci flow is the flow of Riemannian metrics given by the equation

where g is the metric and Ric is the Ricci curvature.

Richard Hamilton first considered this flow in 1981, showing that any 3-manifold which admits a metric of positive curvature, admits a metric of constant curvature as well.

It can be used to prove various important results, like the uniformization theorem or possibly the Thurston's conjecture, which includes the famous Poincaré conjecture.