Fekete points and convergence towards equilibrium measures on complex manifolds

Robert Berman Department of Mathematics, Chalmers University of Technology and University of Göteborg Sébastien Boucksom Institut de Mathématiques, CNRS-Université Pierre et Marie Curie David Witt Nyström Department of Mathematics, Chalmers University of Technology and University of Göteborg

Complex Variables and Complex Analysis Differential Geometry mathscidoc:1701.08001

Acta Mathematica, 207, (1), 1-27, 2009.7
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.
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@inproceedings{robert2009fekete,
  title={Fekete points and convergence towards equilibrium measures on complex manifolds},
  author={Robert Berman, Sébastien Boucksom, and David Witt Nyström},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203357020032743},
  booktitle={Acta Mathematica},
  volume={207},
  number={1},
  pages={1-27},
  year={2009},
}
Robert Berman, Sébastien Boucksom, and David Witt Nyström. Fekete points and convergence towards equilibrium measures on complex manifolds. 2009. Vol. 207. In Acta Mathematica. pp.1-27. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203357020032743.
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