## Univalent harmonic functions

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- by W. Hengartner and G. Schober PDF
- Trans. Amer. Math. Soc.
**299**(1987), 1-31 Request permission

## 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 $\left | z \right | > 1$ 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.## References

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## Additional Information

- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**299**(1987), 1-31 - MSC: Primary 30C45; Secondary 30C50, 31A05
- DOI: https://doi.org/10.1090/S0002-9947-1987-0869396-9
- MathSciNet review: 869396