Pluripotential theory on algebraic curves

TL;DR

This paper advances pluripotential theory on algebraic curves by introducing new Chebyshev constants, relating them to existing ones, and constructing extremal functions to recover the Siciak-Zaharjuta extremal function for compact subsets.

Contribution

It defines a new class of Chebyshev constants, relates them to existing classes, and develops extremal functions for algebraic curves, extending pluripotential theory tools.

Findings

Introduced a second class of Chebyshev constants.

Established relations between the two classes of Chebyshev constants.

Constructed extremal functions to recover the Siciak-Zaharjuta extremal function.

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 $K$.