Minimum Energy Problem on the Hypersphere

We consider the minimum energy problem on the unit sphere $\mathbb S^{d-1}$ in the Euclidean space $\mathbb R^d$, $d\geq 3$, in the presence of an external field $Q$, where the charges are assumed to interact according to Newtonian potential $1/r^{d-2}$, with $r$ denoting the Euclidean distance. We...

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Bibliographic Details
Main Author: Bilogliadov, Mykhailo
Format: Report
Language:unknown
Published: arXiv 2016
Subjects:
Classical Analysis and ODEs math.CA
FOS Mathematics
31B05, 31B10, 31B15
North Pole
Online Access:https://dx.doi.org/10.48550/arxiv.1604.01115
https://arxiv.org/abs/1604.01115
id ftdatacite:10.48550/arxiv.1604.01115
record_format openpolar
spelling ftdatacite:10.48550/arxiv.1604.01115 2023-05-15T17:39:47+02:00 Minimum Energy Problem on the Hypersphere Bilogliadov, Mykhailo 2016 https://dx.doi.org/10.48550/arxiv.1604.01115 https://arxiv.org/abs/1604.01115 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Classical Analysis and ODEs math.CA FOS Mathematics 31B05, 31B10, 31B15 Preprint Article article CreativeWork 2016 ftdatacite https://doi.org/10.48550/arxiv.1604.01115 2022-04-01T11:32:48Z We consider the minimum energy problem on the unit sphere $\mathbb S^{d-1}$ in the Euclidean space $\mathbb R^d$, $d\geq 3$, in the presence of an external field $Q$, where the charges are assumed to interact according to Newtonian potential $1/r^{d-2}$, with $r$ denoting the Euclidean distance. We solve the problem by finding the support of the extremal measure, and obtaining an explicit expression for the density of the extremal measure. We then apply our results to an external field generated by a point charge of positive magnitude, placed at the North Pole of the sphere, and to a quadratic external field. : arXiv admin note: substantial text overlap with arXiv:1510.06420 Report North Pole DataCite Metadata Store (German National Library of Science and Technology) North Pole
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Classical Analysis and ODEs math.CA
FOS Mathematics
31B05, 31B10, 31B15
spellingShingle Classical Analysis and ODEs math.CA
FOS Mathematics
31B05, 31B10, 31B15
Bilogliadov, Mykhailo
Minimum Energy Problem on the Hypersphere
topic_facet Classical Analysis and ODEs math.CA
FOS Mathematics
31B05, 31B10, 31B15
description We consider the minimum energy problem on the unit sphere $\mathbb S^{d-1}$ in the Euclidean space $\mathbb R^d$, $d\geq 3$, in the presence of an external field $Q$, where the charges are assumed to interact according to Newtonian potential $1/r^{d-2}$, with $r$ denoting the Euclidean distance. We solve the problem by finding the support of the extremal measure, and obtaining an explicit expression for the density of the extremal measure. We then apply our results to an external field generated by a point charge of positive magnitude, placed at the North Pole of the sphere, and to a quadratic external field. : arXiv admin note: substantial text overlap with arXiv:1510.06420
format Report
author Bilogliadov, Mykhailo
author_facet Bilogliadov, Mykhailo
author_sort Bilogliadov, Mykhailo
title Minimum Energy Problem on the Hypersphere
title_short Minimum Energy Problem on the Hypersphere
title_full Minimum Energy Problem on the Hypersphere
title_fullStr Minimum Energy Problem on the Hypersphere
title_full_unstemmed Minimum Energy Problem on the Hypersphere
title_sort minimum energy problem on the hypersphere
publisher arXiv
publishDate 2016
url https://dx.doi.org/10.48550/arxiv.1604.01115
https://arxiv.org/abs/1604.01115
geographic North Pole
geographic_facet North Pole
genre North Pole
genre_facet North Pole
op_rights arXiv.org perpetual, non-exclusive license
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
op_doi https://doi.org/10.48550/arxiv.1604.01115
_version_ 1766140555113267200

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