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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Univalent harmonic functions


Authors: W. Hengartner and G. Schober
Journal: Trans. Amer. Math. Soc. 299 (1987), 1-31
MSC: Primary 30C45; Secondary 30C50, 31A05
MathSciNet review: 869396
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Abstract: Several families of complex-valued, univalent, harmonic functions are studied from the point of view of geometric function theory. One class consists of mappings of a simply-connected domain onto an infinite horizontal strip with a normalization at the origin. Extreme points and support points are determined, as well as sharp estimates for Fourier coefficients and distortion theorems. Next, mappings in $ \left\vert z \right\vert > 1$ are considered that leave infinity fixed. Some coefficient estimates, distortion theorems, and covering properties are obtained. For such mappings with real boundary values, many extremal problems are solved explicitly.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0869396-9
PII: S 0002-9947(1987)0869396-9
Keywords: Harmonic mappings, extremal problems
Article copyright: © Copyright 1987 American Mathematical Society