Hyperbolic conemanifolds, short geodesics, and Schwarzian derivatives
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Abstract:
Given a geometrically finite hyperbolic conemanifold, with the conesingularity sufficiently short, we construct a oneparameter family of conemanifolds decreasing the coneangle to zero. We also control the geometry of this oneparameter family via the Schwarzian derivative of the projective boundary and the length of closed geodesics.References

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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
 Received by editor(s): December 10, 2002
 Published electronically: July 21, 2004
 Additional Notes: Supported by a grant from the NSF
 © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.  Journal: J. Amer. Math. Soc. 17 (2004), 783826
 MSC (2000): Primary 30F40, 57M50
 DOI: https://doi.org/10.1090/S089403470400462X
 MathSciNet review: 2083468