In differential geometry,

**Ricci flow**is the flow of Riemannian metrics given by the equation

*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.