Remote Access Conformal Geometry and Dynamics
Green Open Access

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
DOI: https://doi.org/10.1090/S1088-4173-99-00053-3
Published electronically: December 2, 1999
MathSciNet review: 1718708
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $S^n$.


References [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (1991): 30C65, 58F, 53C

Retrieve articles in all journals with MSC (1991): 30C65, 58F, 53C


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: https://doi.org/10.1090/S1088-4173-99-00053-3
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

American Mathematical Society