Is the slit of a rational slit mapping in $S$ straight?
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- by Uri Srebro PDF
- Proc. Amer. Math. Soc. 96 (1986), 65-66 Request permission
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
- Dov Aharonov, A note on slit mappings, Bull. Amer. Math. Soc. 75 (1969), 836–839. MR 259083, DOI 10.1090/S0002-9904-1969-12317-7
- P. L. Duren, Y. J. Leung, and M. M. Schiffer, Support points with maximum radial angle, Complex Variables Theory Appl. 1 (1982/83), no. 2-3, 263–277. MR 690498, DOI 10.1080/17476938308814018
- Zeev Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1952. MR 0045823
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 65-66
- MSC: Primary 30C55; Secondary 30C25
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813811-8
- MathSciNet review: 813811