Collapsing irreducible 3-manifolds with nontrivial fundamental group

2009/11/10 by L. Bessières, Laurent Bessières, G. Besson +7 · 2 citations
Mathematics · #3-manifold #Combinatorics #Conjecture #Curvature #Exact sequence #Fundamental group #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Graph #Manifold (fluid mechanics) #Mathematics #Point processes and geometric inequalities #Pure mathematics #Riemannian manifold #Scalar curvature #Sectional curvature #Simply connected space

paper · doi:10.1007/s00222-009-0222-6

openalex publication_date 2009/11/10 · crossref created 2009/11/10 · crossref issued 2009/11/11 · crossref published 2009/11/11 · crossref published-online 2009/11/11 · crossref published-print 2010/02/01 · crossref deposited 2019/05/24 · openalex created_date 2025/10/10 · crossref indexed 2026/04/18 · openalex updated_date 2026/07/23

Citations

• Three-manifolds with positive Ricci curvature
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Completion of the Proof of the Geometrization Conjecture
• A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow
• A Compactness Property for Solutions of the Ricci Flow
• Volume collapsed three-manifolds with a lower curvature bound
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci flow with surgery on three-manifolds
• Notes on Perelman’s papers
• Ricci Flow and the Poincare Conjecture

Cited by

• A Simple Proof of Perelman’s Collapsing Theorem for 3-manifolds
• Geometrization conjecture [wikipedia]