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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stoïlow factorization for quasiregular mappings in all dimensions


Authors: Gaven Martin and Kirsi Peltonen
Journal: Proc. Amer. Math. Soc. 138 (2010), 147-151
MSC (2000): Primary 30D05; Secondary 37F30
Published electronically: August 12, 2009
MathSciNet review: 2550179
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Abstract: We generalize to higher dimensions the classical Stoïlow factorisation theorem; we show that any quasiregular mapping $ f$ of the Riemann $ n$-sphere $ \hat{\mathbb{R}}^n \approx \mathbb{S}^n$ can be written in the form $ f=\varphi \circ h$, where $ h:\mathbb{S}^n \to \mathbb{S}^n$ is quasiconformal and $ \varphi$ is a uniformly quasiregular mapping, hence rational with respect to some bounded measurable conformal structure.


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Additional Information

Gaven Martin
Affiliation: Department of Mathematics, Massey University, Auckland, New Zealand
Email: G.J.Martin@massey.ac.nz

Kirsi Peltonen
Affiliation: Helsinki University of Technology, P.O. Box 1100, FIN-02015 Espoo, Finland
Email: kirsi.peltonen@tkk.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10056-4
PII: S 0002-9939(09)10056-4
Keywords: Uniformly quasiregular mappings
Received by editor(s): September 14, 2008
Published electronically: August 12, 2009
Communicated by: Mario Bonk
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.