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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
MathSciNet review:
1327008
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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
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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
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