Collapsing three-manifolds under a lower curvature bound

Takashi Shioya, Takao Yamaguchi

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

The purpose of this paper is to completely characterize the topology of threedimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension.

Original languageEnglish
Pages (from-to)1-66
Number of pages66
JournalJournal of Differential Geometry
Volume56
Issue number1
DOIs
Publication statusPublished - 2000 Jan 1

Keywords

  • Alexandrov spaces
  • Seifert fibred spaces
  • The Gromov-Hausdorff convergence
  • Topology of three-manifolds

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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