## Acta Mathematica

### Fekete points and convergence towards equilibrium measures on complex manifolds

#### 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.

#### Article information

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

Dates
Revised: 27 June 2010
First available in Project Euclid: 31 January 2017

https://projecteuclid.org/euclid.acta/1485892567

Digital Object Identifier
doi:10.1007/s11511-011-0067-x

Mathematical Reviews number (MathSciNet)
MR2863909

Zentralblatt MATH identifier
1241.32030

Rights

#### Citation

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. https://projecteuclid.org/euclid.acta/1485892567

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