Locally collapsed 3-manifolds

Bruce Kleiner, John Lott

Research output: Contribution to journalArticlepeer-review


We prove that a 3-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman and was used in his proof of the geometrization conjecture.

Original languageEnglish (US)
Pages (from-to)7-99
Number of pages93
Issue number365
StatePublished - 2014


  • Collapsing
  • Geometrization
  • Orbifold
  • Ricci flow

ASJC Scopus subject areas

  • General Mathematics


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