IUMJ

Title: Chebyshev constants and transfinite diameter on algebraic curves in $\mathbb{C}^2$

Authors: S. Ma'u

Issue: Volume 60 (2011), Issue 5, 1767-1796

Abstract:

Directional Chebyshev constants and transfinite diameter are defined for compact subsets of a complex algebraic curve in $\mathbb{C}^2$. Given such a compact subset $K$, a formula equating the geometric mean of the directional Chebyshev constants of $K$ with its transfinite diameter is proved. This formula generalizes the relation between the classical transfinite diameter and Chebyshev constant in the complex plane, and is a discrete analog of Zaharjuta's integral formula for the Fekete-Leja transfinite diameter in $\mathbb{C}^n$. Further properties of the Chebyshev constants and transfinite diameter are also studied.