Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article

A decomposition theorem for planar harmonic mappings

Author(s): Peter Duren; Walter Hengartner
Journal: Proc. Amer. Math. Soc. 124 (1996), 1191-1195.
MSC (1991): Primary 30C99; Secondary 31A05, 30C65
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: A necessary and sufficient condition is found for a complex-valued harmonic function to be decomposable as an analytic function followed by a univalent harmonic mapping.

References:

1.: W. Hengartner and G. Schober, Harmonic mappings with given dilatation, J. London Math. Soc. 33 (1986), 473--483.MR 87j:30037
2.: O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, 2nd ed., Springer-Verlag, Berlin, Heidelberg, and New York, 1973.MR 49:9202
3.: H. Lewy, On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc. 42 (1936), 689--692.
4.: A. Lyzzaik, Local properties of light harmonic mappings, Canad. J. Math. 44 (1992), 135--153.MR 93e:30048

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C99, 31A05, 30C65

Retrieve articles in all Journals with MSC (1991): 30C99, 31A05, 30C65

Additional Information:

Peter Duren
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: duren@umich.edu

Walter Hengartner
Affiliation: Département de Mathématiques, Université Laval, Québec, P.Q., Canada G1K 7P4
Email: walheng@mat.ulaval.ca

DOI: 10.1090/S0002-9939-96-03319-9
PII: S 0002-9939(96)03319-9
Keywords: Harmonic functions, harmonic mappings, analytic functions, complex dilatation, quasiconformal mappings, Beltrami equation, compositions
Received by editor(s): October 10, 1994
Communicated by: Albert Baernstein II
Copyright of article: Copyright 1996, American Mathematical Society


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS