On the spacing of Fekete points for a sphere, ball or simplex

Suppose that K ⊂ ℝd is either the unit ball, the unit sphere or the standard simplex. We show that there are constants c1, c2 > 0 such that for a set of Fekete points (maximizing the Vandermonde determinant) of degree n, Fn ⊂ K, Figure optionsDownload full-size imageDownload as PowerPoint slide for all a ∈ Fn. Here dist(a, b) is a natural distance on K that will be described in the text.