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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Ends of hyperbolic $3$-manifolds
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by Richard D. Canary PDF
J. Amer. Math. Soc. 6 (1993), 1-35 Request permission

Abstract:

Let $N = {{\mathbf {H}}^3}/\Gamma$ be a hyperbolic $3$-manifold which is homeomorphic to the interior of a compact $3$-manifold. We prove that $N$ is geometrically tame. As a consequence, we prove that $\Gamma$’s limit set ${L_\Gamma }$ is either the entire sphere at infinity or has measure zero. We also prove that $N$’s geodesic flow is ergodic if and only if ${L_\Gamma }$ is the entire sphere at infinity.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 6 (1993), 1-35
  • MSC: Primary 57M50; Secondary 30F40
  • DOI: https://doi.org/10.1090/S0894-0347-1993-1166330-8
  • MathSciNet review: 1166330