On separation of minimal Riesz energy points on spheres in Euclidean spaces

Abstract

Let Sd denote the unit sphere in the Euclidean space Rd + 1 (d ≥ 1). Let N be a natural number (N ≥ 2), and let ωN {colon equals} { x1, ..., xN } be a collection of N distinct points on Sd on which the minimal Riesz s-energy is attained. In this paper, we show that the points x1, ..., xN are well-separated for the cases d - 1 ≤ s < d.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/j.cam.2005.04.074

Keywords

Generalized Thomson problem, Minimal energy, Riesz energy, Separation of mininmal energy points, Spherical potential

Publication Date

2-1-2007

Journal Title

Journal of Computational and Applied Mathematics

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