Volumes of hyperbolic 3-manifolds. Notes on a paper of Gabai, Meyerhoff, and Milley

Marshall, T.; Martin, G.

doi:10.1090/S1088-4173-03-00081-X

Volumes of hyperbolic $3$-manifolds. Notes on a paper of Gabai, Meyerhoff, and Milley
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by T. H. Marshall and G. J. Martin

Conform. Geom. Dyn. 7 (2003), 34-48

DOI: https://doi.org/10.1090/S1088-4173-03-00081-X

Published electronically: 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 $3$-manifolds. We establish the following two facts: if a hyperbolic $3$-manifold admits an embedded tubular neighbourhood of radius $r_0>1.32$ about any closed geodesic, then its volume exceeds that of the Weeks manifold. If the shortest geodesic of $M$ has length less than $\ell _0<0.1$, then its volume also exceeds that of the Weeks manifold.

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