Locally Collapsed 3-Manifolds

Abstract

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.

Final version

References in corpus (1)

• Completion of the Proof of the Geometrization Conjecture

Cited by in corpus (6)

• Geometrization of Three-Dimensional Orbifolds via Ricci Flow
• Partial regularity and smooth topology-preserving approximations of rough domains
• On the topology of locally volume collapsed Riemannian 3-orbifolds
• Long-time analysis of 3 dimensional Ricci flow I
• Collapsing three-dimensional closed Alexandrov spaces with a lower curvature bound
• Perelman's collapsing theorem for 3-manifolds