Collapsing three-manifolds with a lower curvature bound

DOI10.2748/tmj/1325886277zbMath1252.53051OpenAlexW2022487586MaRDI QIDQ765663

Takashi Shioya

Publication date: 21 March 2012

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1325886277

zbMATH Keywords

Alexandrov spacesgeometrization conjecturevolume collapsing theorem

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) General geometric structures on low-dimensional manifolds (57M50) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Cites Work

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• A simple proof of Perelman's collapsing theorem for 3-manifolds
• Notes on Perelman's papers
• Collapsing Riemannian manifolds while keeping their curvature bounded. I
• Bounding homotopy types by geometry
• Collapsing and pinching under a lower curvature bound
• The fundamental groups of almost nonnegatively curved manifolds
• A generalized sphere theorem
• The Riemannian structure of Alexandrov spaces
• Mass of rays in Alexandrov spaces of nonnegative curvature
• Collapsing three-manifolds under a lower curvature bound.
• Geometric finiteness theorems via controlled topology
• On the structure of complete manifolds of nonnegative curvature
• Volume collapsed three-manifolds with a lower curvature bound
• Collapsing irreducible 3-manifolds with nontrivial fundamental group
• Nilpotent Structures and Invariant Metrics on Collapsed Manifolds
• A.D. Alexandrov spaces with curvature bounded below
• Almost flat manifolds

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