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Discrete quasiconformal groups that are not the quasiconformal conjugates of Möbius groups. (English) Zbl 0635.30021
From the introduction: The author provides examples of discrete quasiconformal groups that are not the quasiconformal conjugates of Möbius groups. Gehring and Palka asked in 1976 whether every such group was in fact the quasiconformal conjugate of a conformal, or Möbius, group.
In the case of quasiconformal groups acting on subsets of the Riemann sphere the question was answered in the affirmative by Sullivan and Tukia. Later Tukia has given examples of quasiconformal groups of \({\bar {\mathbb{R}}}^ n\), \(n\geq 3\), which were not the quasiconformal conjugates of any Möbius group. His examples were not discrete and the present author constructs quasiconformal groups which are discrete, too.
Reviewer: M.Vuorinen

MSC:
30C62 Quasiconformal mappings in the complex plane
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