Volumes of tubes in hyperbolic 3-manifolds

David Gabai, Robert Meyerhoff, Peter Milley

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We give the first explicit lower bound for the length of a geodesic in a closed orientable hyperbolic 3-manifold M of lowest volume. We also give an upper bound for the tube radius of any shortest geodesic in M. We explain how these results might be the first steps towards a rigorous computer assisted effort to determine the least volume closed orientable hyperbolic 3-manifold(s).

Original languageEnglish (US)
Pages (from-to)23-46
Number of pages24
JournalJournal of Differential Geometry
Volume57
Issue number1
DOIs
StatePublished - Jan 1 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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