Ricci flow

Summary

The Ricci flow is the evolution equation $\partial_t g = -2 \operatorname{Ric}(g)$ for a family of Riemannian metrics on a manifold. It was introduced by Richard Hamilton in 1982. It is a nonlinear, weakly parabolic system that behaves like a heat equation for the metric, smoothing out irregularities of the curvature. Grigori Perelman used the Ricci flow with surgery to prove the Poincaré conjecture and Thurston's geometrization conjecture.