Koebe sequences of arcs and normal meromorphic functions
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- by Stephen Dragosh PDF
- Trans. Amer. Math. Soc. 190 (1974), 207-222 Request permission
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 ${C^\ast }$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- 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