Cluster points and asymptotic values of planar harmonic functions
Complex Variables
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0508624,
title = {Cluster points and asymptotic values of planar harmonic functions},
author = {Genevra Neumann},
journal= {arXiv preprint arXiv:math/0508624},
year = {2007}
}
Comments
13 pages