## Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives

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- by K. Bromberg
- J. Amer. Math. Soc.
**17**(2004), 783-826 - DOI: https://doi.org/10.1090/S0894-0347-04-00462-X
- Published electronically: July 21, 2004
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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.## References

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## Bibliographic 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), 783-826 - MSC (2000): Primary 30F40, 57M50
- DOI: https://doi.org/10.1090/S0894-0347-04-00462-X
- MathSciNet review: 2083468