Acta Mathematica

, Volume 207, Issue 1, pp 1–27

Fekete points and convergence towards equilibrium measures on complex manifolds

  • Robert Berman
  • Sébastien Boucksom
  • David Witt Nyström
Article

DOI: 10.1007/s11511-011-0067-x

Cite this article as:
Berman, R., Boucksom, S. & Nyström, D.W. Acta Math (2011) 207: 1. doi:10.1007/s11511-011-0067-x

Abstract

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.

Copyright information

© Institut Mittag-Leffler 2011

Authors and Affiliations

  • Robert Berman
    • 1
  • Sébastien Boucksom
    • 2
  • David Witt Nyström
    • 1
  1. 1.Department of MathematicsChalmers University of Technology and University of GöteborgGöteborgSweden
  2. 2.Institut de MathématiquesCNRS-Université Pierre et Marie CurieParis Cedex 05France