Tohoku Mathematical Journal
2011
December
SECOND SERIES VOL. 63, NO. 4

Tohoku Math. J.
63 (2011), 471-487

Title COLLAPSING THREE-MANIFOLDS WITH A LOWER CURVATURE BOUND

Author Takashi Shioya

(Received August 31, 2010, revised March 3, 2011)
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.

2000 Mathematics Subject Classification. Primary 53C23; Secondary 53C20, 57M50.
Key words and phrases. The volume collapsing theorem, Alexandrov spaces, the geometrization conjecture.

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