Ricci flow

In differential geometry, the Ricci flow (/ˈriːtʃi/, Italian: [ˈrittʃi]) is an intrinsic geometric flow. It is 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.

The Ricci flow, named after Gregorio Ricci-Curbastro, was first introduced by Richard S. Hamilton in 1981 and is also referred to as the Ricci–Hamilton flow. It is the primary tool used in Grigori Perelman's solution of the Poincaré conjecture, as well as in the proof of the differentiable sphere theorem by Simon Brendle and Richard Schoen.