Tohoku Mathematical Journal

Collapsing three-manifolds with a lower curvature bound

Takashi Shioya

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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

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

First available in Project Euclid: 6 January 2012

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Zentralblatt MATH identifier

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

The volume collapsing theorem Alexandrov spaces the geometrization conjecture


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.

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