On the equilibrium measure and the capacity of certain condensers

Abstract

We prove some geometric estimates for the equilibrium measure and the capacity of certain condensers. The proofs are based on the interpretation of the equilibrium measure as the distributional Laplacian of the corresponding potential, on a formula of T. Bagby, and on a method of Beurling and Nevanlinna that involves the transport of the Riesz mass of a superharmonic function.