Minimal Riesz Energy on the Sphere for Axis-supported External Fields
نویسندگان
چکیده
We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere S 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| with d−2 ≤ s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on S is determined. The special case s = d − 2 yields interesting phenomena, which we investigate in detail. A weak asymptotic analysis is provided as s → (d − 2).
منابع مشابه
Riesz extremal measures on the sphere for axis-supported external fields
We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere S 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| with d−2 ≤ s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on S i...
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