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EQUIDISTRIBUTION RATE FOR FEKETE POINTS ON SOME REAL MANIFOLDS

Vu, Duc-Viet

American journal of mathematics, 2018-10, Vol.140 (5), p.1311-1355 [Periódico revisado por pares]

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Título:
EQUIDISTRIBUTION RATE FOR FEKETE POINTS ON SOME REAL MANIFOLDS
Autor: Vu, Duc-Viet
Assuntos: Configurations ; Convergence ; Fix-point estimation ; Hyperplanes ; Manifolds (Mathematics) ; Set theory
É parte de: American journal of mathematics, 2018-10, Vol.140 (5), p.1311-1355
Descrição: 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 Lk 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 C5-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 Rn or the unitsphere in Rn+1.
Editor: Baltimore: Johns Hopkins University Press
Idioma: Inglês

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