Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C55, 30H05

Retrieve articles in all journals with MSC: 30C55, 30H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0656110-6
Article copyright: © Copyright 1982 American Mathematical Society