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

DOI:
https://doi.org/10.1090/S0002-9939-00-05765-8

Published electronically:
November 30, 2000

MathSciNet review:
1825913

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-00-05765-8

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