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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quasiconformal groups with small dilatation I


Authors: Petra Bonfert-Taylor and Gaven Martin
Journal: Proc. Amer. Math. Soc. 129 (2001), 2019-2029
MSC (1991): Primary 30F40, 57S30, 30C65, 20H10
Published electronically: November 30, 2000
MathSciNet review: 1825913
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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.


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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
Email: bonfert@math.lsa.umich.edu, pbonfert@wesleyan.edu

Gaven Martin
Affiliation: Department of Mathematics, University of Auckland, New Zealand
Email: martin@math.auckland.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05765-8
PII: S 0002-9939(00)05765-8
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
Article copyright: © Copyright 2000 American Mathematical Society