Trees as Level Sets for Pseudoharmonic Functions in the Plane

Author: Polulyakh E.  

Publisher: Springer Publishing Company

ISSN: 0041-5995

Source: Ukrainian Mathematical Journal, Vol.65, Iss.7, 2013-12, pp. : 1087-1110

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Abstract

Let T be a finite or infinite tree and let V 0 be the set of all vertices of T of valency 1. We propose a sufficient condition for the image of the imbedding ψ: T V 0$ {{mathbb{R}}^2} $ to be a level set of a pseudoharmonic function.