Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30C45, 30C50, 31A05

Retrieve articles in all journals with MSC: 30C45, 30C50, 31A05

Additional Information

PII: S 0002-9947(1987)0869396-9
Keywords: Harmonic mappings, extremal problems
Article copyright: © Copyright 1987 American Mathematical Society