Journal of Differential Geometry

Volumes of Tubes in Hyperbolic 3-Manifolds

David Gabai, G. Robert Meyerhoff, and Peter Milley

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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).

Article information

Source
J. Differential Geom., Volume 57, Number 1 (2001), 23-46.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090348088

Digital Object Identifier
doi:10.4310/jdg/1090348088

Mathematical Reviews number (MathSciNet)
MR1871490

Zentralblatt MATH identifier
1029.57014

Citation

Gabai, David; Meyerhoff, G. Robert; Milley, Peter. Volumes of Tubes in Hyperbolic 3-Manifolds. J. Differential Geom. 57 (2001), no. 1, 23--46. doi:10.4310/jdg/1090348088. https://projecteuclid.org/euclid.jdg/1090348088


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