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Hyperbolic Metric and Multiply Connected Wandering Domains of Meromorphic Functions

Published online by Cambridge University Press:  30 January 2017

Jian-Hua Zheng*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China ([email protected])

Abstract

In this paper, in terms of the hyperbolic metric, we give a condition under which the image of a hyperbolic domain of an analytic function contains a round annulus centred at the origin. From this, we establish results on the multiply connected wandering domains of a meromorphic function that contain large round annuli centred at the origin. We thereby successfully extend the results of transcendental meromorphic functions with finitely many poles to those with infinitely many poles.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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