复流形上的Fekete点与收敛于平衡测度

Fekete点在均匀多项式尖点集上的收敛速度

Convergence Speed for Fekete Points on Uniformly Polynomially Cuspidal Sets

研究Fekete点在均匀多项式尖点集上的收敛速度，通过证明这些集在Dinh、Ma和Nguyen的意义下是$(\mathscr{C}^α, \mathscr{C}^{α'})$-正则的。

Equidistribution speed for Fekete points associated with an ample line bundle

Let K be the closure of a bounded open set with smooth boundary in C^n. A Fekete configuration of order p for K is a finite subset of K maximizing the Vandermonde determinant associated with polynomials of degree at most p. A recent theorem by Berman, Boucksom and Witt Nystrom implies that Fekete configurations for K are asymptotically equidistributed with respect to a canonical equilibrium measure, as p tends to infinite. We give here an explicit estimate for the speed of convergence. The result also holds in a general setting of Fekete points associated with an ample line bundle over a proje…

Weighted Fekete points on the real line and the unit circle

Weighted Fekete points are defined as those that maximize the weighted version of the Vandermonde determinant over a fixed set. They can also be viewed as the equilibrium distribution of the unit discrete charges in an external electrostatic field. While these points have many applications, they are very difficult to find explicitly, and are only known in a few (unweighted) classical cases. We give two rare explicit examples of weighted Fekete points. The first one is for the weights $w(x)=|x-ai|^{-s}$ on the real line, with $s\ge 1$ and $a\neq 0,$ while the second is for the weights $w(z)=1/|…

Equidistribution rate for Fekete points on some real manifolds

Let L be a positive line bundle over a compact complex projective manifold X and K be a compact subset of X 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 tends to infinity. Dinh, Ma and Nguyen obtained an estimate for the rate of convergence. Using techniques from Cauchy-Riemann geometry, we show that…

全纯截面球体在紧黎曼面上的增长速率

Growth rate of balls of holomorphic sections on compact Riemann surfaces

研究全纯截面球体在紧黎曼面上的增长速率及Fekete测度收敛速度，采用能量平衡方法分析。

Extremal potentials and equilibrium measures associated to collections of Kähler classes

Given a collection of Kähler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equilibrium measures which coincide with classical notions when the collection is a singleton. We prove two regularity results and set up a variational framework. Applications to Fekete points are treated elsewhere.