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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The extreme points of $\Sigma$


Author: D. H. Hamilton
Journal: Proc. Amer. Math. Soc. 85 (1982), 393-396
MSC: Primary 30C55; Secondary 30H05
DOI: https://doi.org/10.1090/S0002-9939-1982-0656110-6
MathSciNet review: 656110
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Abstract: For any compact set in ${\mathbf {C}}$, with complement $\Omega$ which contains $\infty$ and is connected the class $\Sigma$ consists of functions $g(z) = z + {b_1}{z^{ - 1}} + \cdots$ that are univalent in $\Omega$. We prove that $g \in \Sigma$ is an extreme point of $\Sigma$ if and only if ${\mathbf {C}} - g(\Omega )$ has zero area.


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Article copyright: © Copyright 1982 American Mathematical Society