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 Free Access
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 
.
- [HM] A. Hinkkanen and G. J. Martin, Attractors in quasiregular semigroups, XVIth Rolf Nevanlinna Colloquium (Joensuu, 1995) de Gruyter, Berlin, 1996, pp. 135–141. MR 1427078
- [IM] Tadeusz Iwaniec and Gaven Martin, Quasiregular semigroups, Ann. Acad. Sci. Fenn. Math. 21 (1996), no. 2, 241–254. MR 1404085
- [KS] R. C. Kirby and M. G. Scharlemann, Eight faces of the Poincaré homology 3-sphere, Geometric topology (Proc. Georgia Topology Conf., Athens, Ga., 1977), Academic Press, New York-London, 1979, pp. 113–146. MR 537730
- [M] G. J. Martin, Branch sets of uniformly quasiregular maps, Conform. Geom. Dyn. 1 (1997), 24–27. MR 1454921, https://doi.org/10.1090/S1088-4173-97-00016-7
- [MM] G.J. Martin and V. Mayer, Rigidity in holomorphic and quasiregular dynamics. Preprint.
- [Mo] José María Montesinos, Classical tessellations and three-manifolds, Universitext, Springer-Verlag, Berlin, 1987. MR 915761
- [P] K. Peltonen, Quasiregularity on homology manifolds, MLI preprint no 14, 95/96.
- [R] Seppo Rickman, Quasiregular mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 26, Springer-Verlag, Berlin, 1993. MR 1238941
- [TV] P. Tukia and J. Väisälä, Lipschitz and quasiconformal approximation and extension, Ann. Acad. Sci. Fenn. Ser. A I Math. 6 (1981), no. 2, 303–342 (1982). MR 658932, https://doi.org/10.5186/aasfm.1981.0626
- [W] Joseph A. Wolf, Spaces of constant curvature, McGraw-Hill Book Co., New York-London-Sydney, 1967. MR 0217740
-sphere, Proc. of Geometric Topology Conference, Athens, 1979. 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
