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Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives

Bromberg, K. (2004) Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives. Journal of the American Mathematical Society, 17 (4). pp. 783-826. ISSN 0894-0347. doi:10.1090/S0894-0347-04-00462-X.

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Given a geometrically finite hyperbolic cone-manifold, with the cone-singularity sufficiently short, we construct a one-parameter family of cone-manifolds decreasing the cone-angle to zero. We also control the geometry of this one-parameter family via the Schwarzian derivative of the projective boundary and the length of closed geodesics.

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Additional Information:© 2004 American Mathematical Society. Received by the editors December 10, 2002. Posted: July 21, 2004. Supported by a grant from the NSF.
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Subject Keywords:Kleinian groups, cone-manifolds, Schwarzian derivative. Supported by a grant from the NSF.
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MathSciNet review: 2083468
Issue or Number:4
Classification Code:2000 Mathematics Subject Classi�cation. Primary 30F40, 57M50.
Record Number:CaltechAUTHORS:20110916-095139469
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Official Citation:Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives K. Bromberg J. Amer. Math. Soc. 17 (2004), 783-826.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:25351
Deposited By: Ruth Sustaita
Deposited On:16 Sep 2011 17:49
Last Modified:09 Nov 2021 16:32

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