Acta Mathematica

Fekete points and convergence towards equilibrium measures on complex manifolds

Robert Berman, Sébastien Boucksom, and David Witt Nyström

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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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Acta Math., Volume 207, Number 1 (2011), 1-27.

Received: 16 July 2009
Revised: 27 June 2010
First available in Project Euclid: 31 January 2017

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2011 © Institut Mittag-Leffler


Berman, Robert; Boucksom, Sébastien; Nyström, David Witt. Fekete points and convergence towards equilibrium measures on complex manifolds. Acta Math. 207 (2011), no. 1, 1--27. doi:10.1007/s11511-011-0067-x.

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