On Separation of Minimal Riesz Energy Points on Spheres in Euclidean Spaces

Kuijlaars, A. B. J.; Saff, E. B.; Sun, X.

On Separation of Minimal Riesz Energy Points on Spheres in Euclidean Spaces

Authors

Kuijlaars, A. B. J.

Saff, E. B.

Sun, X.

Description

For the unit sphere S^d in Euclidean space R^(d+1), we show that for d-1<s<d and any N>1, discrete N-point minimal Riesz s-energy configurations are well separated in the sense that the minimal distance between any pair of distinct points in such a configuration is bounded below by C/N^(1/d), where C is a positive constant depending on s and d.
12 pages, submitted to Irsee Conference Proceedings