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UNIVALENT HARMONIC MAPPINGS INTO TWO-SLIT DOMAINS

Part of: Geometric function theory

Published online by Cambridge University Press:  22 January 2010

ANDRZEJ GANCZAR  and
JAROSŁAW WIDOMSKI
ANDRZEJ GANCZAR*
Affiliation:
Institute of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland (email: aganczar@hektor.umcs.lublin.pl)
JAROSŁAW WIDOMSKI
Affiliation:
Institute of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland (email: jwidomski@hektor.umcs.lublin.pl)
*
✉For correspondence; e-mail: aganczar@hektor.umcs.lublin.pl
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Abstract

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We study some classes of planar harmonic mappings produced with the shear construction devised by Clunie and Sheil-Small in 1984. The first section reviews the basic concepts and describes the shear construction. The main body of the paper deals with the geometry of the classes constructed.

Keywords

univalent harmonic mappingsshear construction

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 1 , February 2010 , pp. 61 - 73
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Clunie, J. and Sheil-Small, T., ‘Harmonic univalent functions’, Ann. Acad. Sci. Fenn. Ser. A. I Math. 9 (1984), 3–25.CrossRefGoogle Scholar
[2]Hengartner, W. and Schober, G., ‘Univalent harmonic functions’, Trans. Amer. Math. Soc. 299(1) (1987), 1–31.CrossRefGoogle Scholar
[3]Lewy, H., ‘On the non-vanishing of the Jacobian in certain one-to-one mappings’, Bull. Amer. Math. Soc. 42 (1936), 689–692.CrossRefGoogle Scholar
[4]Livingston, A. E., ‘Univalent harmonic mappings’, Ann. Polon. Math. LVII(1) (1992), 57–70.CrossRefGoogle Scholar
[5]Royster, W. C. and Ziegler, M., ‘Univalent functions convex in one direction’, Publ. Math. Debrecen 23(3–4) (1976), 339–345.CrossRefGoogle Scholar