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

2005/03/27 by A. B. J. Kuijlaars, E. B. Saff, Kuijlaars, A. B. J. +3
Mathematics · Physics and Astronomy · #11K41 #28A78 #70F50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP #msc:11K41 #msc:28A78 #msc:70F50

paper · pdf · doi:10.48550/arxiv.math-ph/0503063

12 pages, submitted to Irsee Conference Proceedings

arxiv created 2005/03/27 · arxiv updated 2009/12/01

Abstract

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.

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