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December, 2005 Quasiconformal groups of compact type
Petra Bonfert-Taylor, Gaven Martin
Rev. Mat. Iberoamericana 21(3): 997-1012 (December, 2005).

Abstract

We establish that a quasiconformal group is of compact type if and only if its limits set is purely conical and find that the limit set of a quasiconformal group of compact type is uniformly perfect. A key tool is the result of Bowditch-Tukia on compact-type convergence groups. These results provide crucial tools for studying the deformations of quasiconformal groups and in establishing isomorphisms between such groups and conformal groups.

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Petra Bonfert-Taylor. Gaven Martin. "Quasiconformal groups of compact type." Rev. Mat. Iberoamericana 21 (3) 997 - 1012, December, 2005.

Information

Published: December, 2005
First available in Project Euclid: 11 January 2006

zbMATH: 1281.30033
MathSciNet: MR2232673

Subjects:
Primary: 20H10 , 30C65 , 30F40 , 57S30

Keywords: conical limit set , convergence groups , geometric finiteness , quasiconformal groups

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.21 • No. 3 • December, 2005
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