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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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 |
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DataCite Metadata Store (German National Library of Science and Technology) |
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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 |
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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 |