Noun
Ricci flow (plural Ricci flows)
(differential geometry) A process that deforms the metric of a Riemannian manifold in a way formally analogous to the diffusion of heat, smoothing out irregularities in the metric.
A special case of Perelman's theorems about Ricci flow with surgery is given as follows. Source: Internet
But today, the Poincaré conjecture has been proven using time as a mathematical concept in which objects can flow (see Ricci flow ). Source: Internet
Completing the proof, Perelman takes any compact, simply connected, three-dimensional manifold without boundary and starts to run the Ricci flow. Source: Internet
Hamilton had shown that the area of a minimal surface decreases as the manifold undergoes Ricci flow. Source: Internet
Hamilton used the Ricci flow to prove that some compact manifolds were diffeomorphic to spheres and he hoped to apply it to prove the Poincaré Conjecture. Source: Internet
He wanted to cut the manifold at the singularities and paste in caps, and then run the Ricci flow again, so he needed to understand the singularities and show that certain kinds of singularities do not occur. Source: Internet