What is Ricci flow?
The '''Ricci flow''' ({{IPAc-en|ˈ|r|iː|tʃ|i}} {{respell|REE|chee}}, {{IPA-it|ˈrittʃi|lang}}) is a [[partial differential equation]] used in [[differential geometry]] and [[geometric analysis]]. It is like the [[heat equation]], which is used to study [[diffusion|diffusion of heat]]. The Ricci flow is named for the [[Ricci tensor]], which is part of its definition. [[Richard S. Hamilton|Richard Hamilton]] used the Ricci flow in the 1980s to prove new results in [[Riemannian geometry]]. Later, other mathematicians used it to solve the [[differentiable sphere theorem|differentiable sphere conjecture]]. In the 1990s, Hamilton used the Ricci flow to study [[William Thurston]]'s [[geometrization conjecture]]. In 2002 and 2003, [[Grigori Perelman]] made new discoveries about the Ricci flow. These discoveries, along with Hamilton's work, are now seen as a proof of the Thurston conjecture, and of the [[Poincaré conjecture]], which had been an open problem since 1904. This work is a major milestone in the fields of [[geometry]] and [[topology]]. [[Image:Ricci flow.png|thumb|right|upright|200px|Several stages of Ricci flow on a 2D manifold.]] [[Category:Differential geometry]]