Trees as Level Sets for Pseudoharmonic Functions in the Plane

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.