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arXiv · 0902.1558

Minimal Riesz energy on the sphere for axis-supported external fields

J. S. Brauchart·P. D. Dragnev·E. B. Saff
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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)^+.

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J. S. Brauchart, P. D. Dragnev, E. B. Saff. 2009-02-09. Minimal Riesz energy on the sphere for axis-supported external fields. https://doi.org/10.1016/j.jmaa.2009.03.060

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