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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Examples of uniformly quasiregular mappings


Author: Kirsi Peltonen
Journal: Conform. Geom. Dyn. 3 (1999), 158-163
MSC (1991): Primary 30C65, 58F; Secondary 53C
Published electronically: December 2, 1999
MathSciNet review: 1718708
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Abstract: In this paper we construct examples of uniformly quasiregular (uqr) mappings. These provide counterexamples for a rigidity conjecture in quasiregular dynamics. It states that a closed manifold of dimension at least three, which admits a branched uqr mapping, is quasiconformally equivalent to an ordinary sphere $S^n$.


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Additional Information

Kirsi Peltonen
Affiliation: Helsinki University of Technology, Department of Engineering Physics and Mathematics, P.O. Box 1100, 02015 HUT, Finland
Email: Kirsi.Peltonen@hut.fi

DOI: http://dx.doi.org/10.1090/S1088-4173-99-00053-3
PII: S 1088-4173(99)00053-3
Keywords: Uniformly quasiregular mappings, quasiregular dynamics, branched covering
Received by editor(s): July 26, 1999
Received by editor(s) in revised form: October 27, 1999
Published electronically: December 2, 1999
Article copyright: © Copyright 1999 American Mathematical Society