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Optimal subtrees of finite metric graphs

  • Levi Haunschmid-Sibitz
  • Fredrik Viklund
  • David Witt Nyström
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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.

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Cite

BibTeXRIS
BibTeX
@misc{haunschmidsibitz2026optimal,
  title = {{Optimal subtrees of finite metric graphs}},
  author = {Levi Haunschmid-Sibitz and Fredrik Viklund and David Witt Nyström},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40168},
  eprint = {2610.40168},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40168},
}
RIS
TY  - UNPB
TI  - Optimal subtrees of finite metric graphs
AU  - Levi Haunschmid-Sibitz
AU  - Fredrik Viklund
AU  - David Witt Nyström
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40168
UR  - https://arxiv.org/abs/2610.40168
AB  - 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.
ER  -