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Proceedings of the American Mathematical Society

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

 

 

Harmonic measure and conformal length


Author: Knut Øyma
Journal: Proc. Amer. Math. Soc. 115 (1992), 687-689
MSC: Primary 30C35
MathSciNet review: 1101991
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Abstract: Let $ f(z)$ be any univalent function that maps the unit disc onto a domain $ \Omega $. We prove that for any line $ L$ the length of $ {f^{ - 1}}(\Omega \cap L)$ is less than $ 4\pi $.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1101991-1
Keywords: Harmonic measure, univalent function
Article copyright: © Copyright 1992 American Mathematical Society