Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective

2006/10/29 by Terence Tao, Tao, Terence · 1 voice · 2 citations
Mathematics · #53C44 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:53C44

paper · pdf · doi:10.48550/arxiv.math/0610903

42 pages, unpublished

arxiv created 2006/10/29 · openalex publication_date 2006/10/29 · arxiv published 2006/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On the parabolic kernel of the Schrödinger operator
• A Compactness Property for Solutions of the Ricci Flow
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci flow with surgery on three-manifolds

Cited by

• Minimally invasive surgery for Ricci flow singularities
• Perelman's functional and reduced volume

Discussions

• Perelman's Proof of the Poincar E Conjecture: A Nonlinear PDE Perspective [hn, 2 points, 0 comments]

Related

• Ricci Flow and the Poincare Conjecture
• Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture
• Perelman, Poincare, and the Ricci Flow
• Ricci flow on Poincare' and Thurston's Geometrization Conjecture
• Simple proofs of some results of Perelman on Ricci flow