Volume collapsed three-manifolds with a lower curvature bound

2005/06/22 by Takashi Shioya, Takao Yamaguchi · 5 citations
Mathematics · #Combinatorics #Curvature #Curvature of Riemannian manifolds #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Mathematical analysis #Mathematics #Minimal volume #Physics #Point processes and geometric inequalities #Pure mathematics #Ricci curvature #Ricci-flat manifold #Scalar curvature #Sectional curvature #Topology (electrical circuits) #Upper and lower bounds #Volume (thermodynamics)

paper · doi:10.1007/s00208-005-0667-x

crossref issued 2005/06/22 · crossref published 2005/06/22 · crossref published-online 2005/06/22 · openalex publication_date 2005/06/22 · crossref created 2005/06/27 · crossref published-print 2005/09/01 · crossref deposited 2020/04/07 · openalex created_date 2025/10/10 · crossref indexed 2026/04/18 · openalex updated_date 2026/07/23

Citations

• Ricci flow with surgery on three-manifolds

Cited by

• Collapsing irreducible 3-manifolds with nontrivial fundamental group
• A Simple Proof of Perelman’s Collapsing Theorem for 3-manifolds
• Perelman’s Stability Theorem
• Recent progress on the Poincaré conjecture and the classification of 3-manifolds
• Perspectives on geometric analysis
• Notes on Perelman’s papers
• Geometrization conjecture [wikipedia]