Ricci Flow
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 Poincaré conjecture; in this context is also called the Ricci Hamilton flow.The Ricci flow (named after Gregorio Ricci-Curbastro) was introduced by R...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 Poincaré conjecture; in this context is also called the Ricci Hamilton flow.The Ricci flow (named after Gregorio Ricci-Curbastro) was introduced by Richard Hamilton in 1981 in order to gain insight into the geometrization conjecture of William Thurston, which concerns the topological classification of three-dimensional smooth manifolds. Hamilton''s idea was to define a kind of nonlinear diffusion equation which would tend to smooth out irregularities in the metric. Then, by placing an arbitrary metric g on a given smooth manifold M and evolving the metric by the Ricci flow, the metric should approach a particularly nice metric, which might constitute a canonical form for M.
