Conical plurisubharmonic measure and new cross theorems

Let L be a positive line bundle over a compact complex projective manifold X and K ⊂ X be a compact set which is regular in a sense of pluripotential theory. A Fekete configuration of order k is a finite subset of K maximizing a Vandermonde type determinant associated with the power L k of L. Berman, Boucksom and Witt Nyström proved that the empirical measure associated with a Fekete configuration converges to the equilibrium measure of K as k → ∞. Dinh, Ma and Nguyen obtained an estimate for the rate of convergence. Using techniques from Cauchy-Riemann geometry, we show that the last result holds when K is a real nondegenerate C 5 -piecewise submanifold of X such that its tangent space at any regular point is not contained in a complex hyperplane of the tangent space of X at that point. In particular, the estimate holds for Fekete points on some compact sets in R n or the unit sphere in R n+1 . Classification AMS 2010: 32U15.

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A unified approach to the theory of separately holomorphic mappings

Nguyên¹

2009

Annali Scuola Normale Superiore - Classe Di Scienze

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We extend the theory of separately holomorphic mappings between complex analytic spaces. Our method is based on Poletsky theory of discs, Rosay theorem on holomorphic discs and our recent joint-work with Pflug on boundary cross theorems in dimension 1. It also relies on our new technique of conformal mappings and a generalization of Siciak's relative extremal function. Our approach illustrates the unified character: "From local information to global extensions". Moreover, it avoids systematically the use of the classical method of doubly orthogonal bases of Bergman type.

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Conical plurisubharmonic measure and new cross theorems

Abstract: We study the boundary behavior of the conical plurisubharmonic measure. As an application, we establish some new extension theorems for separately holomorphic mappings defined on cross sets.

Cited by 3 publications

References 6 publications

Corrigendum to “Conical plurisubharmonic measure and new cross theorems” [J. Math. Anal. Appl. 365 (2010) 429–434]

Corrigendum to “Conical plurisubharmonic measure and new cross theorems” [J. Math. Anal. Appl. 365 (2010) 429–434]

Equidistribution rate for Fekete points on some real manifolds

A unified approach to the theory of separately holomorphic mappings

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