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Univalent Harmonic Ring Mappings Vanishing on the Interior Boundary

Published online by Cambridge University Press:  20 November 2018

Walter Hengartner  and
Jan Szynal
Walter Hengartner
Affiliation:
Département de Mathématiques Université LavalQuébec G1K 7P4
Jan Szynal
Affiliation:
Département de Mathématiques Université LavalQuébec G1K 7P4
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Abstract

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We give a characterization of univalent positively oriented harmonic mappings ƒ defined on an exterior neighbourhood of the closed unit disk { z: | z| ≤1} such that .

Keywords

30C55
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 2 , 01 April 1992 , pp. 308 - 323
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Bers, L., Theory of pseudo-analytic functions, Lecture notes (mimeographed), New York University 1953; An outline of the theory of pseudo-analytic functions, Bull. Amer. Math. Soc. 62(1956), 291–331.Google Scholar
2. Dundu, L.E.čenko, Certain extremal properties of analytic functions given in a circle and in a circular ring, Ukrain. Mat. ž., 8(1956), 377–325.Google Scholar
3. Hengartner, W. and Schober, G., Harmonic mappings with given dilation, J. London Mat. Soc. (2) 33(1986), 473–483.Google Scholar
4. Hengartner, W., Univalent harmonic exterior and ring mappings, J. Math. Anal. Appl. 156(1991), 154–171.Google Scholar
5. Komatu, Y., On analytic functions with positive real part in an annulus, Kodai Math. Rep. 10(1958), 84–100.Google Scholar
6. Livingston, A.E. and Pfaltzgraff, J.A., Structure and extremal problems for classes of functions analytic in an annulus, Colloq. Math., 43(1980), 161–181.Google Scholar
7. Zmorovi, V.A.č, On some classes of analytic functions in a circular ring, Mat. Sc. 32(74) (1953), 633–652.Google Scholar