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

19 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

Access to Document

10.4310/jdg/1090348088

Cite this

@article{3e8d3575887741648757980efe02f362,

title = "Volumes of tubes in hyperbolic 3-manifolds",

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).",

author = "David Gabai and Robert Meyerhoff and Peter Milley",

year = "2001",

doi = "10.4310/jdg/1090348088",

language = "English (US)",

volume = "57",

pages = "23--46",

journal = "Journal of Differential Geometry",

issn = "0022-040X",

publisher = "International Press of Boston, Inc.",

number = "1",

}

TY - JOUR

T1 - Volumes of tubes in hyperbolic 3-manifolds

AU - Gabai, David

AU - Meyerhoff, Robert

AU - Milley, Peter

PY - 2001

Y1 - 2001

N2 - 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).

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).

UR - http://www.scopus.com/inward/record.url?scp=0012683710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012683710&partnerID=8YFLogxK

U2 - 10.4310/jdg/1090348088

DO - 10.4310/jdg/1090348088

M3 - Article

AN - SCOPUS:0012683710

SN - 0022-040X

VL - 57

SP - 23

EP - 46

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 1

ER -

Volumes of tubes in hyperbolic 3-manifolds

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this