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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Koebe sequences of arcs and normal meromorphic functions


Author: Stephen Dragosh
Journal: Trans. Amer. Math. Soc. 190 (1974), 207-222
MSC: Primary 30A72
DOI: https://doi.org/10.1090/S0002-9947-1974-0338376-5
MathSciNet review: 0338376
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Abstract: Let f be a normal meromorphic function in the unit disk. An estimate for the growth of the modulus of f on a Koebe sequence of arcs is obtained; the estimate is in terms of the order of normality of f. An immediate consequence of the estimate is the following theorem due to F. Bagemihl and W. Seidel: A nonconstant normal meromorphic function has no Koebe values. Another consequence is that each level set of a nonconstant normal meromorphic function cannot contain a Koebe sequence of arcs provided the order of normality of f is less than a certain positive constant $ {C^\ast}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0338376-5
Keywords: Normal meromorphic function, order of normality, Koebe lemma, Koebe sequence of arcs, level set, boundary behavior
Article copyright: © Copyright 1974 American Mathematical Society