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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The limit sets of Schottky quasiconformal groups are uniformly perfect


Author: Xiaosheng Li
Journal: Trans. Amer. Math. Soc. 357 (2005), 2119-2132
MSC (2000): Primary 30C65
DOI: https://doi.org/10.1090/S0002-9947-05-03870-5
Published electronically: January 27, 2005
MathSciNet review: 2140434
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Abstract: In this paper we study Schottky quasiconformal groups. We show that the limit sets of Schottky quasiconformal groups are uniformly perfect, and that the limit set of a given discrete non-elementary quasiconformal group has positive Hausdorff dimension.


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Additional Information

Xiaosheng Li
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
Address at time of publication: Division of Science & Mathematics, University of Minnesota, Morris, 600 East 4th Street, Morris, Minnesota 56267
Email: xli5@math.uiuc.edu, lixiao@umn.edu

DOI: https://doi.org/10.1090/S0002-9947-05-03870-5
Keywords: Schottky quasiconformal group, uniformly perfect
Received by editor(s): July 23, 2002
Published electronically: January 27, 2005
Article copyright: © Copyright 2005 American Mathematical Society