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Is the slit of a rational slit mapping in $ S$ straight?

Author: Uri Srebro
Journal: Proc. Amer. Math. Soc. 96 (1986), 65-66
MSC: Primary 30C55; Secondary 30C25
MathSciNet review: 813811
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Abstract: The question in the title is answered by showing that if $ f$ is a rational function in $ {\mathbf{\hat C}}$ and maps some disk injectively onto the complement of a set $ E$ of empty interior, then $ \operatorname{degree}(f) = 2$, and $ E$ is either a circular arc or a line segment in $ {\mathbf{\hat C}} = {\mathbf{C}} \cup \{ \infty \} $.

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

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  • [3] Z. Nehari, Conformal mapping, McGraw-Hill, New York, 1952. MR 0045823 (13:640h)

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Keywords: Univalent functions, slit functions, Koebe functions, rational functions
Article copyright: © Copyright 1986 American Mathematical Society

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