Revista Matemática Iberoamericana

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Volume 21, Issue 3, 2005, pp. 997–1012
DOI: 10.4171/RMI/442

Published online: 2005-12-31

Quasiconformal groups of compact type

Petra Bonfert-Taylor[1] and Gaven J. Martin[2]

(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. Iberoam. 21 (2005), 997-1012. doi: 10.4171/RMI/442