Robert BermanDepartment of Mathematics, Chalmers University of Technology and University of GöteborgSébastien BoucksomInstitut de Mathématiques, CNRS-Université Pierre et Marie CurieDavid Witt NyströmDepartment of Mathematics, Chalmers University of Technology and University of Göteborg
Complex Variables and Complex AnalysisDifferential Geometrymathscidoc:1701.08001
Building on [BB1] we prove a general criterion for convergence of (possibly singular) Bergman measures towards pluripotential-theoretic equilibrium measures on complex manifolds. The criterion may be formulated in terms of the growth properties of the unit-balls of certain norms on holomorphic sections, or equivalently as an asymptotic minimization property for generalized Donaldson$L$-functionals. Our result settles in particular a well-known conjecture in pluripotential theory concerning the equidistribution of Fekete points and it gives the convergence of Bergman measures towards the equilibrium measure for Bernstein-Markov measures. Applications to interpolation of holomorphic sections are also discussed.