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

Email:
bromberg@math.utah.edu

DOI:
http://dx.doi.org/10.1090/S0894-0347-04-00462-X

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.