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2011 Fekete points and convergence towards equilibrium measures on complex manifolds
Robert Berman, Sébastien Boucksom, David Witt Nyström
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Acta Math. 207(1): 1-27 (2011). DOI: 10.1007/s11511-011-0067-x


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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Robert Berman. Sébastien Boucksom. David Witt Nyström. "Fekete points and convergence towards equilibrium measures on complex manifolds." Acta Math. 207 (1) 1 - 27, 2011.


Received: 16 July 2009; Revised: 27 June 2010; Published: 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1241.32030
MathSciNet: MR2863909
Digital Object Identifier: 10.1007/s11511-011-0067-x

Rights: 2011 © Institut Mittag-Leffler

Vol.207 • No. 1 • 2011
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