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arXiv · 2601.07639

Pluripotential theory on algebraic curves

Norm Levenberg·Sione Ma'u
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Abstract

In previous works, the second author defined directional Robin constants associated to a compact, nonpolar subset $K$ of an algebraic curve $A$ in $\mathbb{C}^N$ and related these to a natural class of Chebyshev constants for $K$. We define a second class of Chebyshev constants for $K$; relate these two classes; and utilize each of them to define two families of extremal-like functions which can be used to recover the Siciak-Zaharjuta extremal function for $K$.

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Norm Levenberg, Sione Ma'u. 2026-01-20. Pluripotential theory on algebraic curves. https://arxiv.org/abs/2601.07639

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