Extremal potentials and equilibrium measures associated to collections of K\"ahler classes

Abstract

Given a collection of K\"ahler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equilibrium measures which coincide with classical notions when the collection is a singleton. We prove two regularity results and set up a variational framework. Applications to Fekete points are treated elsewhere.