Computational Methods and Function Theory 7 (2007), No. 1, 249--263
Copyright Heldermann Verlag 2007
Genevra Neumann
neumann@math.uni.edu , Kansas State University, Department of Mathematics, Manhattan, KS 66506-2602, U.S.A.
A sufficient condition for a cluster point of a C1-function on R2 to be an asymptotic value is given, based on a partitioning into regions of constant valence. We also obtain a sufficient condition for the cluster set of a planar harmonic function to have non-empty interior. 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: Planar harmonic functions, C1-function in R2, cluster set, asymptotic values.
MSC 2000: Primary 30C99, 26B99; Secondary 31A05, 26C99.
[FullText-pdf (279 K)] [FullText-ps (476 K)]