Revista Matemática Iberoamericana
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Published online: 2005-12-31
Quasiconformal groups of compact typePetra Bonfert-Taylor and Gaven J. Martin (1) Wesleyan University, Middletown, USA
(2) Massey University, Auckland, New Zealand
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.
Keywords: Quasiconformal groups, convergence groups, geometric finiteness, conical limit set
Bonfert-Taylor Petra, Martin Gaven: Quasiconformal groups of compact type. Rev. Mat. Iberoamericana 21 (2005), 997-1012. doi: 10.4171/RMI/442