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arXiv · 2608.15722

Characterisation of some multivalued harmonic functions on $\mathbb{R}^{n}$

Yang Li·Parsa Mashayekhi·Yichen Zhang
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Abstract

Using different approaches, Simon Donaldson and Dashen Yan recently constructed $\mathbb Z_2$-harmonic functions on $\mathbb R^3$ and on $\mathbb R^n$ for $n\geqslant 3$, respectively. Their examples have quadratic growth at infinity and $\mathcal{O}(r^{3/2})$ local growth near a smooth codimension-two branching set $\Sigma$. We show that these properties uniquely characterise such $\mathbb Z_2$-harmonic functions up to rigid motions of $\mathbb R^n$.

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Yang Li, Parsa Mashayekhi, Yichen Zhang. 2026-08-16. Characterisation of some multivalued harmonic functions on $\mathbb{R}^{n}$. https://arxiv.org/abs/2608.15722

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