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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Regions of variability for univalent functions


Authors: Peter Duren and Ayşenur Ünal
Journal: Trans. Amer. Math. Soc. 295 (1986), 119-126
MSC: Primary 30C70
MathSciNet review: 831192
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Abstract: Let $ S$ be the standard class of univalent functions in the unit disk, and let $ {S_0}$ be the class of nonvanishing univalent functions $ g$ with $ g(0) = 1$. It is shown that the regions of variability $ \{ g(r):g \in {S_0}\} $ and $ \{ (1 - {r^2})f\prime(r):f \in S\} $ are very closely related but are not quite identical.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0831192-5
Keywords: Univalent functions, regions of variability, extremal problems, variational methods, quadratic differentials, algebraic curves
Article copyright: © Copyright 1986 American Mathematical Society