Mystery of point charges

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dc.creatorGabrielov, Andrei
dc.creatorNovikov, Dmitry
dc.creatorShapiro, Boris
dc.date2004-09-03
dc.date.accessioned2026-07-07T04:31:26Z
dc.date.available2026-07-07T04:31:26Z
dc.descriptionWe discuss the problem of finding an upper bound for the number of equilibrium points of a potential of several fixed point charges in R^n. This question goes back to J.C.Maxwell and M.Morse. Using fewnomial theory we show that for a given number of charges there exists an upper bound independent on the dimension, and show it to be 12 for three charges. We conjecture the exact upper bound for a given configuration of nonnegative charges in terms of its Voronoi diagram, and prove it asymptotically.
dc.descriptionLatex, 29 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0409009
dc.identifierhttp://arxiv.org/abs/math-ph/0409009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57811
dc.subjectMathematical Physics
dc.subjectPrimary 31B05; Secondary 58E05
dc.titleMystery of point charges
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