Volumes of hyperbolic manifolds. Notes on a paper of Gabai, Meyerhoff, and Milley
Authors:
T. H. Marshall and G. J. Martin
Journal:
Conform. Geom. Dyn. 7 (2003), 3448
MSC (2000):
Primary 30F40, 30D50, 57M50
Published electronically:
June 17, 2003
MathSciNet review:
1992036
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We present a new approach and improvements to the recent results of Gabai, Meyerhoff and Milley concerning tubes and short geodesics in hyperbolic manifolds. We establish the following two facts: if a hyperbolic manifold admits an embedded tubular neighbourhood of radius about any closed geodesic, then its volume exceeds that of the Weeks manifold. If the shortest geodesic of has length less than , then its volume also exceeds that of the Weeks manifold.
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 17.
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Additional Information
T. H. Marshall
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand
Email:
t_marshall@math.auckland.ac.nz
G. J. Martin
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand
Email:
martin@math.auckland.ac.nz
DOI:
http://dx.doi.org/10.1090/S108841730300081X
PII:
S 10884173(03)00081X
Received by editor(s):
August 30, 2001
Received by editor(s) in revised form:
April 10, 2003
Published electronically:
June 17, 2003
Additional Notes:
Research supported in part by the N. Z. Marsden Fund and the N. Z. Royal Society (James Cook Fellowship)
Article copyright:
© Copyright 2003 American Mathematical Society
