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Infinitely many asymptotic values of locally univalent functions

Barth, Karl F. and Rippon, Philip J. (2003). Infinitely many asymptotic values of locally univalent functions. Annales Academiae Scientiarum Fennicae Mathematica, 28 pp. 303–314.

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Abstract

McMillan and Pommerenke showed that a locally univalent meromorphic function $f$ in the disc, without Koebe arcs, has at least three asymptotic values in each boundary arc. The modular function shows that the number three is best possible. We show that if $f$ satisfies certain further conditions, each of which narrowly excludes the modular function, then the number of asymptotic values in each boundary arc must be infinite.

Item Type: Journal Article
ISSN: 1239-629X
Keywords: locally univalent; asymptotic value; Koebe arcs
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 3625
Depositing User: Philip Rippon
Date Deposited: 30 Jun 2006
Last Modified: 13 Jul 2011 14:48
URI: http://oro.open.ac.uk/id/eprint/3625
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