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Trees as Level Sets for Pseudoharmonic Functions in the Plane

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Ukrainian Mathematical Journal Aims and scope

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.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 974–995, July, 2013.

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Polulyakh, E.O. Trees as Level Sets for Pseudoharmonic Functions in the Plane. Ukr Math J 65, 1087–1110 (2013). https://doi.org/10.1007/s11253-013-0844-0

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  • DOI: https://doi.org/10.1007/s11253-013-0844-0

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