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

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