Monotonicity formulas for harmonic functions on the infinite regular tree
Analysis of PDEs
2026-03-16 v1
Abstract
We continue the program initiated in \cite{SVGS}. In this paper, we focus on the infinite regular tree, and prove the monotonicity of a weighted Dirichlet energy, a Weiss-type monotonicity formula, and a generalization of the Almgren monotonicity formula of \cite{SVGS} for . We also compute examples in the infinite and regular trees.
Keywords
Cite
@article{arxiv.2603.13132,
title = {Monotonicity formulas for harmonic functions on the infinite regular tree},
author = {Kathryn Atwood and Mariana Smit Vega Garcia and Richard Wang},
journal= {arXiv preprint arXiv:2603.13132},
year = {2026}
}