Optimal subtrees of finite metric graphs

Abstract

We consider a metric graph analog of a classical extremal problem for Riemann surfaces studied by Teichmüller, Jenkins, Strebel, and others. In particular, we prove that on any finite metric graph with a marked point, there is a unique open subtree which maximizes a metric graph analog of the reduced modulus, and we also give an equivalent characterization of this optimal subtree in terms of balanced harmonic measures.

arXiv comment13 pages. No AI tools were used