Ends of hyperbolic 3-manifolds
- 1 January 1993
- journal article
- Published by American Mathematical Society (AMS) in Journal of the American Mathematical Society
- Vol. 6 (1) , 1-35
- https://doi.org/10.1090/s0894-0347-1993-1166330-8
Abstract
Let N = H 3 / Γ N = {{\mathbf {H}}^3}/\Gamma be a hyperbolic 3 3 -manifold which is homeomorphic to the interior of a compact 3 3 -manifold. We prove that N N is geometrically tame. As a consequence, we prove that Γ \Gamma ’s limit set L Γ {L_\Gamma } is either the entire sphere at infinity or has measure zero. We also prove that N N ’s geodesic flow is ergodic if and only if L Γ {L_\Gamma } is the entire sphere at infinity.Keywords
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