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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A uniqueness result in conformal mapping. II


Author: James A. Jenkins
Journal: Proc. Amer. Math. Soc. 85 (1982), 231-232
MSC: Primary 30C55
MathSciNet review: 652448
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Abstract: This paper gives an elementary proof of the result that for a function $ f$ in the family $ \Sigma $ the diameter of the complement of the image of $ \left\vert z \right\vert > 1$ by $ w = f(z)$ attains its minimal value 2 only for $ f(z) = z + c$, $ c$ constant.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0652448-7
PII: S 0002-9939(1982)0652448-7
Article copyright: © Copyright 1982 American Mathematical Society