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- Title
EQUIDISTRIBUTION RATE FOR FEKETE POINTS ON SOME REAL MANIFOLDS.
- Authors
DUC-VIET VU
- Abstract
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 unit sphere in Rn+1.
- Subjects
SET theory; MANIFOLDS (Mathematics); PLURIPOTENTIAL theory (Mathematics); STOCHASTIC convergence; MATHEMATICAL proofs
- Publication
American Journal of Mathematics, 2018, Vol 140, Issue 5, p1311
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.2018.0033