Conformal Geometry and Dynamics

Author(s): Kirsi Peltonen
Journal: Conform. Geom. Dyn. 3 (1999), 158-163.
MSC (1991): Primary 30C65; Secondary 53C
Posted: December 2, 1999
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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

[HM]: A. Hinkkanen and G.J. Martin, Attractors in quasiregular semigroups. Proc. XVI Nevanlinna colloquim, Eds. I. Laine and O. Martio, de Gruyter, Berlin-New York, 1996, 135-141. MR 97m:30028
[IM]: T. Iwaniec and G.J. Martin, Quasiregular semigroups, Ann. Acad. Sci. Fenn. 21, 1996, 241-254. MR 97i:30032
[KS]: R. Kirby and M. Scharlemann, Eight faces of Poincaré homology $3$ -sphere, Proc. of Geometric Topology Conference, Athens, 1979. MR 80k:57042
[M]: G.J. Martin, Branch sets of uniformly quasiregular maps, Conformal Geometry and Dynamics 1, 24-27. MR 98d:30032
[MM]: G.J. Martin and V. Mayer, Rigidity in holomorphic and quasiregular dynamics. Preprint.
[Mo]: J.M. Montesinos, Classical tessellations and three-manifolds, Springer-Verlag, 1987. MR 89d:57016
[P]: K. Peltonen, Quasiregularity on homology manifolds, MLI preprint no 14, 95/96.
[R]: S. Rickman, Quasiregular mappings, Springer-Verlag, 1993. MR 95g:30026
[TV]: P. Tukia and J. Väisälä, Lipschitz and quasiconformal approximation and extension, Ann. Acad. Sci. Fenn. Ser. A I Math. 6, 1981, 303-342. MR 84a:57016
[W]: J.A. Wolf, Spaces of constant curvature, McGraw-Hill, 1967. MR 36:829

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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: 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
Posted: December 2, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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