Hamilton-Perelman's Proof of the Poincar\'e Conjecture and the Geometrization Conjecture

By Huaihuo Cao, Xiping Zhu. 2006

48 citations recorded by the source corpus.

In this paper, we provide an essentially self-contained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of three-manifolds. In particular, we give a detailed exposition of a complete proof of the Poincare conjecture due to Hamilton and Perelman.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a29f4a498d984fff197caf383b5432fef3be275c

Citations in the corpus

• A Compactness Theorem for Complete Ricci Shrinkers (2010, unknown): “(1.2) Then the gradient shrinker has a well defined entropy , The entropy was introduced by Perelman in his famous paper [30] to solve the long standing problem of ruling out collapsing with bounded curvature (see [4, 9, 25, 28] for detailed expositions of Perelman’s work).”