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Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives

Author: K. Bromberg
Journal: J. Amer. Math. Soc. 17 (2004), 783-826
MSC (2000): Primary 30F40, 57M50
Published electronically: July 21, 2004
MathSciNet review: 2083468
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Abstract: 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

K. Bromberg
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112

Keywords: Kleinian groups, cone-manifolds, Schwarzian derivative
Received by editor(s): December 10, 2002
Published electronically: July 21, 2004
Additional Notes: Supported by a grant from the NSF
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.