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Title: Minimal Riesz energy on the sphere for axis-supported external fields
Authors: Brauchart, J. S.Dragnev, P. D.Saff, E. B.
Publishers Version:
Issue Date: 2009
Published in: Oberwolfach preprints (OWP), Volume 2009-04, ISSN 1864-7596
Publisher: Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach
Abstract: 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)+.
Keywords: Balayage; Equilibrium Measures; Extremal Measures; Minimum Energy; Riesz kernel; Weighted Energy
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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