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Quasiconformal groups of compact type.

Petra Bonfert-Taylor, Gaven Martin (2005)

Revista Matemática Iberoamericana

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.

Quasiconformal mappings of Y-pieces.

Christopher J. Bishop (2002)

Revista Matemática Iberoamericana

In this paper we construct quasiconformal mappings between Y-pieces so that the corresponding Beltrami coefficient has exponential decay away from the boundary. These maps are used in a companion paper to construct quasiFuchsian groups whose limit sets are non-rectifiable curves of dimension 1.

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