High Quality Content by WIKIPEDIA articles! In differential geometry, the Ricci flow is an intrinsic geometric flow (a process which deforms the metric of a Riemannian manifold) in this case in a manner formally analogous to the diffusion of heat, thereby smoothing out irregularities in the metric. It plays an important role in Grigori Perelman's solution of the Poincare conjecture; in this context is also called the Ricci–Hamilton flow. The Ricci flow has been intensively studied since 1981.For instance, acertain class of solutions to the Ricci flow demonstrates that neckpinch singularities will form on an evolving n-dimensional metric Riemannian manifold having a certain topological property (positive Euler characteristic), as the flow approaches some characteristic time t0. In certain cases, such neckpinches will produce manifolds called Ricci solitons. There are many related geometric flows, some of which (such as the Yamabe flow and the Calabi flow) have properties similar to the Ricci flow.

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