Collapsing three-manifolds under a lower curvature bound

Takashi Shioya, Takao Yamaguchi

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2000


  • 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


Dive into the research topics of 'Collapsing three-manifolds under a lower curvature bound'. Together they form a unique fingerprint.

Cite this