Collapsing three-manifolds with a lower curvature bound

Takashi Shioya

doi:10.2748/tmj/1325886277

Collapsing three-manifolds with a lower curvature bound

Takashi Shioya

SCI - Mathematics

Research output: Contribution to journal › Review article › peer-review

Abstract

We survey works on collapsing Riemannian manifolds with a lower bound of sectional curvature, focusing on the three-dimensional case. We also explain the basics of Seifert manifolds and Alexandrov spaces quickly and a key idea of our proof of the volume collapsing theorem.

Original language	English
Pages (from-to)	471-487
Number of pages	17
Journal	Tohoku Mathematical Journal
Volume	63
Issue number	4
DOIs	https://doi.org/10.2748/tmj/1325886277
Publication status	Published - 2011 Dec

Keywords

Alexandrov spaces
The geometrization conjecture
The volume collapsing theorem

ASJC Scopus subject areas

Mathematics(all)

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10.2748/tmj/1325886277

Cite this

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abstract = "We survey works on collapsing Riemannian manifolds with a lower bound of sectional curvature, focusing on the three-dimensional case. We also explain the basics of Seifert manifolds and Alexandrov spaces quickly and a key idea of our proof of the volume collapsing theorem.",

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KW - The volume collapsing theorem

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Collapsing three-manifolds with a lower curvature bound

Abstract

Keywords

ASJC Scopus subject areas

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