Supports of Weighted Equilibrium Measures: Complete Characterization

Abstract

In this paper, we prove that a compact set $K\subset {\mathbb{C}}^n$ is the support of a weighted equilibrium measure if and only it is not pluripolar at each of its points extending a result of Saff and Totik to higher dimensions. Thus, we characterize the supports weighted equilibrium measures completely. Our proof is a new proof even in one dimension.

5 pages