Supports of Weighted Equilibrium Measures: Complete Characterization
  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. 
Muhammed Ali Alan, Nihat Gokhan Gogus
math.CV