2005/08/31 by Genevra Neumann, Neumann, Genevra
Mathematics · #26B99 #30C99 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:26B99 #msc:30C99
paper · pdf · doi:10.48550/arxiv.math/0508624
13 pages
arxiv created 2005/08/31 · arxiv updated 2009/12/01
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.