In differential geometry, the Ricci flow 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 was first introduced by Richard 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 Brendle and Schoen.
Read more about Ricci Flow: Mathematical Definition, Examples, Relationship To Uniformization and Geometrization, Relation To Diffusion, Recent Developments
Famous quotes containing the word flow:
“The method of painting is the natural growth out of a need. I want to express my feelings rather than illustrate them. Technique is just a means of arriving at a statement.... I can control the flow of paint: there is no accident, just as there is no beginning and no end.”
—Jackson Pollock (1912–1956)