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Cluster points and asymptotic values of planar harmonic functions

Genevra Neumann
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Abstract

A sufficient condition for a cluster point of a planar harmonic function to be an asymptotic value is given, based on a partitioning into regions of constant valence. A sufficient condition for the cluster set of a planar harmonic function to have non-empty interior is given. An example is given of a planar harmonic function where the image of the critical set is not closed and such that the cluster set has non-empty interior and is a proper subset of the image.

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Genevra Neumann. 2005-08-31. Cluster points and asymptotic values of planar harmonic functions. https://arxiv.org/abs/math/0508624

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