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End date: 2009 × Start date: 2000 × Has files: Yes × Type: Text × Subject: Balayage × WGL Institute: MFO ×

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    Minimal Riesz energy on the sphere for axis-supported external fields
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Brauchart, J.S.; Dragnev, P.D.; Saff, E.B.
    We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere Sd 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 Sd 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)+.