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Grigori Perelman. On November 13, 2002, Russian mathematician Grigori Perelman posted the first of a series of three eprints on arXiv outlining a solution of the Poincaré conjecture. Perelman's proof uses a modified version of a Ricci flow program developed by Richard S. Hamilton.
Abstract. In this paper, we give a complete proof of the Poincar´e and the geometrization conjectures. This work depends on the accumulative works of many geometric analysts in the past thirty years. This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow. Key words.
Grisha Perelman announced a proof of the Poincar´e Conjecture, and more generally Thurston’s Geometrization Conjecture, using the Ricci flow approach of Hamilton. Perelman’s proofs are concise and, at times, sketchy. The purpose of these notes is to provide the details that are missing in[46]and[47], which contain Perelman’s
Dec 22, 2006 · The Poincaré Conjecture--Proved. This article has a correction. To mathematicians, Grigori Perelman's proof of the Poincaré conjecture qualifies at least as the Breakthrough of the Decade. But it has taken them a good part of that decade to convince themselves that it was for real.
Oct 29, 2006 · Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective. We discuss some of the key ideas of Perelman's proof of Poincaré's conjecture via the Hamilton program of using the Ricci flow, from the perspective of the modern theory of nonlinear partial differential equations.
In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston’s geometrization conjecture. Perelman’s proof tells us that every three manifold is built from a set of standard pieces ...
On 22 December 2006, the journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics.[2] . He has since ceased working on mathematics.
