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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A decomposition theorem
for planar harmonic mappings

Authors: Peter Duren and Walter Hengartner
Journal: Proc. Amer. Math. Soc. 124 (1996), 1191-1195
MSC (1991): Primary 30C99; Secondary 31A05, 30C65
MathSciNet review: 1327008
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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 [Enhancements On Off] (What's this?)

  • 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

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Additional Information

Peter Duren
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Walter Hengartner
Affiliation: Département de Mathématiques, Université Laval, Québec, P.Q., Canada G1K 7P4

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
Article copyright: © Copyright 1996 American Mathematical Society