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The limiting behavior of sequences of quasiconformal mappings. (English) Zbl 0699.30016
The limiting behaviour of sequences of K-quasiconformal homeomorphisms of the n-sphere \(S^ n\) is studied using a substitute to the Poincaré extension of Möbius transformations introduced by Tukia. Adapted versions of the limit set and the conical limit set known in the theory of Kleinian groups are shown to play a crucial role. Most of the results hold for families of homeomorphisms of \(S^ n\) which have the convergence property inroduced by Gehring and Martin.
Reviewer: B.Aebischer

MSC:
30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
40A99 Convergence and divergence of infinite limiting processes
Keywords:
Kleinian groups
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