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), 34-48

MSC (2000):
Primary 30F40, 30D50, 57M50

Published electronically:
June 17, 2003

MathSciNet review:
1992036

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Abstract | References | Similar Articles | 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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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/S1088-4173-03-00081-X

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