Fekete Potentials and Polynomials for Continua

Abstract

For planar continua, upper and lower bounds are given for the growth of the associated Fekete potentials, polynomials and energies. The main result is that for continua K of capacity 1 whose outer boundary is an analytic Jordan curve, the family of Fekete polynomials is bounded on K . Our work makes use of precise results of Pommerenke on the growth of the discriminant and on the distribution of the Fekete points. We also use potential theory, including the exterior Green function with pole at infinity. The Lipschitz character of this function determines the separation of the Fekete points.