Minimal Riesz energy on the sphere for axis-supported external fields
Mathematical Physics
2014-02-17 v1 math.MP
Abstract
We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere S^d in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials |x-y|^(-s) with d-2 <= s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on S^d is determined. The special case s = d-2 yields interesting phenomena, which we investigate in detail. A weak* asymptotic analysis is provided as s goes to (d-2)^+.
Cite
@article{arxiv.0902.1558,
title = {Minimal Riesz energy on the sphere for axis-supported external fields},
author = {J. S. Brauchart and P. D. Dragnev and E. B. Saff},
journal= {arXiv preprint arXiv:0902.1558},
year = {2014}
}
Comments
42 pages, 2 figures