Quasiconformal groups with small dilatation I
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- by Petra Bonfert-Taylor and Gaven Martin PDF
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Abstract:
We study Fuchsian quasiconformal groups with small dilatation. For this class of groups we establish a Jørgensen-type inequality in all dimensions. We show discreteness persists to the limit under algebraic convergence and that such groups are discrete if and only if every two generator subgroup is discrete.References
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Additional Information
- Petra Bonfert-Taylor
- Affiliation: Department of Mathematics, The University of Michigan, Ann Arbor, Michigan 48109-1109
- Address at time of publication: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
- MR Author ID: 617474
- Email: bonfert@math.lsa.umich.edu, pbonfert@wesleyan.edu
- Gaven Martin
- Affiliation: Department of Mathematics, University of Auckland, New Zealand
- MR Author ID: 120465
- Email: martin@math.auckland.ac.nz
- Received by editor(s): April 16, 1999
- Received by editor(s) in revised form: November 9, 1999
- Published electronically: November 30, 2000
- Additional Notes: The first author acknowledges research support in part by a University of Michigan Rackham fellowship.
The second author acknowledges research support in part by a grant from the NZ Marsden Fund. - Communicated by: Albert Baernstein II
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2019-2029
- MSC (1991): Primary 30F40, 57S30, 30C65, 20H10
- DOI: https://doi.org/10.1090/S0002-9939-00-05765-8
- MathSciNet review: 1825913