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math.CV2005
Cluster points and asymptotic values of planar harmonic functions
Genevra Neumann
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…
math.CV2004
Valence of complex-valued planar harmonic functions
Genevra Neumann
The valence of a function at a point is the number of distinct, finite solutions to . Let be a complex-valued harmonic function in an open set $R \subseteq \m…
math.CV2004★ 1 cited
On the number of zeros of certain rational harmonic functions
Dmitry Khavinson, Genevra Neumann
Extending a result from the paper of D. Khavinson and G. Swiatek, we show that the rational harmonic function , where r(z) is a rational function of degree n > 1, h…