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arXiv · 2603.13132

Monotonicity formulas for harmonic functions on the infinite regular tree

Kathryn Atwood·Mariana Smit Vega Garcia·Richard Wang
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Abstract

We continue the program initiated in \cite{SVGS}. In this paper, we focus on the infinite $d-$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 $p\ge 1$. We also compute examples in the infinite $2-$ and $3-$regular trees.

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Kathryn Atwood, Mariana Smit Vega Garcia, Richard Wang. 2026-03-13. Monotonicity formulas for harmonic functions on the infinite regular tree. https://arxiv.org/abs/2603.13132

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