Volumes of tubes in hyperbolic 3-manifolds

David Gabai; Robert Meyerhoff; Peter Milley

doi:10.4310/jdg/1090348088

Volumes of tubes in hyperbolic 3-manifolds

David Gabai, Robert Meyerhoff, Peter Milley

Research output: Contribution to journal › Article › peer-review

20 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 language	English (US)
Pages (from-to)	23-46
Number of pages	24
Journal	Journal of Differential Geometry
Volume	57
Issue number	1
DOIs	https://doi.org/10.4310/jdg/1090348088
State	Published - 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology

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10.4310/jdg/1090348088

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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).",

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AU - Meyerhoff, Robert

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AB - 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).

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DO - 10.4310/jdg/1090348088

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SP - 23

EP - 46

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 1

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Volumes of tubes in hyperbolic 3-manifolds

Abstract

All Science Journal Classification (ASJC) codes

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