Collapsing three-manifolds with a lower curvature bound

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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.

Original languageEnglish
Pages (from-to)471-487
Number of pages17
JournalTohoku Mathematical Journal
Volume63
Issue number4
DOIs
Publication statusPublished - 2011 Dec 1

Keywords

  • Alexandrov spaces
  • The geometrization conjecture
  • The volume collapsing theorem

ASJC Scopus subject areas

  • Mathematics(all)

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