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- W4300468692 abstract "In 1984, Gehring and Pommerenke proved that if the Schwarzian derivative $S(f)$ of a locally univalent analytic function $f$ in the unit disk satisfies that $limsup_{|z|to 1} |S(f)(z)| (1-|z|^2)^2 < 2$, then there exists a positive integer $N$ such that $f$ takes every value at most $N$ times. Recently, Becker and Pommerenke have shown that the same result holds in those cases when the function $f$ satisfies that $limsup_{|z|to 1} |f(z)/f'(z)|, (1-|z|^2)< 1$. In this paper, we generalize these two criteria for bounded valence of analytic functions to the cases when $f$ is merely harmonic." @default.
- W4300468692 created "2022-10-03" @default.
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- W4300468692 date "2016-11-17" @default.
- W4300468692 modified "2023-10-18" @default.
- W4300468692 title "Criteria for bounded valence of harmonic mappings" @default.
- W4300468692 doi "https://doi.org/10.48550/arxiv.1611.05667" @default.
- W4300468692 hasPublicationYear "2016" @default.
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