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The Limiting Behavior of Sequences of Quasiconformal Mappings

Published online by Cambridge University Press:  20 November 2018

Beat Aebischer
Beat Aebischer*
Affiliation:
Yale University Department of Mathematics Box 2155, Yale Station New Haven, CT 06520 USA
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Abstract

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The limiting behavior of sequences of quasiconformal homeomorphisms of the n-sphere Sn 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 utilized. Most of the results also hold for families of homeomorphisms of Sn with the convergence property introduced by Gehring and Martin.

Keywords

Primary 30C6040A9930F40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 494 - 502
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Aebischer, B., The limiting behavior of sequences of Möbius transformations, Math. Z. 205 (1990) 49–59.Google Scholar
2. Gehring, F. W. and Martin, G. J., Discrete quasiconformal groups I, Proc. London Math. Soc. 55 (1987), 331–358.Google Scholar
3. Jacobsen, L., General convergence of continued fractions, Trans. Amer. Math. Soc. 294 (1986), 477– 485.Google Scholar
4. Jacobsen, L. and Thron, W. J., Limiting structures for sequences of linear fractional transformations, Proc. Amer. Math. Soc. 99 (1987) 141–146.Google Scholar
5. Tukia, P., Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group, Acta Math. 154(1985), 153–193.Google Scholar
6. Tukia, P., On quasiconformal groups, J. d'Analyse Math. 46 (1986), 318–346.Google Scholar
7. Tukia, P. and J. Väisälä, Quasiconformal extension from dimension n to n +1, Annals of Math. 115 (1982) 331–348.Google Scholar
8. J. Väisälà, Lectures on n-Dimensional Quasiconformal Mappings, Lecture Notes in Mathematics 229, Springer-Verlag, 1971.Google Scholar