Fekete points and convergence towards equilibrium measures on complex manifolds
Fekete points and convergence towards equilibrium measures on complex manifolds
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DOI：
10.1007/s11511-011-0067-x
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发表时间：
2009-07
期刊：
影响因子：
3.7
通讯作者：
R. Berman;S. Boucksom;David Witt Nyström
中科院分区：
文献类型：
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作者：
R. Berman;S. Boucksom;David Witt Nyström
在[BB1]的基础上，我们证明了复流形上Bergman测度（可能是奇异的）向多势理论平衡测度收敛的一般准则。该判据可以用全纯截面上某些范数的单位球的生长性质来表示，或者等价地用广义donaldsonl泛函的渐近极小化性质来表示。我们的结果特别解决了多势理论中关于Fekete点均分的一个著名猜想，并给出了Bergman测度对Bernstein-Markov测度的均衡测度的收敛性。讨论了在全纯截面插值中的应用。
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 DonaldsonL-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.