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