Conformal Geometry and Dynamics

Volumes of hyperbolic

-manifolds. Notes on a paper of Gabai, Meyerhoff, and Milley

Author(s): T. H. Marshall; G. J. Martin
Journal: Conform. Geom. Dyn. 7 (2003), 34-48.
MSC (2000): Primary 30F40, 30D50, 57M50
Posted: June 17, 2003
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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 $\ell_0<0.1$ , then its volume also exceeds that of the Weeks manifold.

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T. H. Marshall
Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand
Email: t_marshall@math.auckland.ac.nz

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