Tohoku Mathematical Journal

Collapsing three-manifolds with a lower curvature bound

Takashi Shioya

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 63, Number 4 (2011), 471-487.

Dates
First available in Project Euclid: 6 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1325886277

Digital Object Identifier
doi:10.2748/tmj/1325886277

Mathematical Reviews number (MathSciNet)
MR2872952

Zentralblatt MATH identifier
1252.53051

Subjects
Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 57M50: Geometric structures on low-dimensional manifolds

Keywords
The volume collapsing theorem Alexandrov spaces the geometrization conjecture

Citation

Shioya, Takashi. Collapsing three-manifolds with a lower curvature bound. Tohoku Math. J. (2) 63 (2011), no. 4, 471--487. doi:10.2748/tmj/1325886277. https://projecteuclid.org/euclid.tmj/1325886277


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