Trees as Level Sets for Pseudoharmonic Functions in the Plane

• Date: 2013
• Main Authors: Polulyakh, E. O., Полулях, Є. О.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2483
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.