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Mystery of point charges
Purdue University.
Weizmann Institute of Science.
Stockholm University, Faculty of Science, Department of Mathematics.
2007 (English)In: Proceedings of the London Mathematical Society, ISSN 0024-6115, E-ISSN 1460-244X, Vol. 95, no 2, 443-472 p.Article in journal (Refereed) Published
Abstract [en]

We discuss the problem of finding an upper bound for the number of equilibrium points of a potential of several fixed point charges in Rn. This question goes back to J. C. Maxwell [10] and M. Morse [12]. Using fewnomial theory we show that for a given number of charges there exists an upper bound independent of the dimension, and show it to be at most 12 for three charges. We conjecture an exact upper bound for a given configuration of nonnegative charges in terms of its Voronoi diagram, and prove it asymptotically.

Place, publisher, year, edition, pages
2007. Vol. 95, no 2, 443-472 p.
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URN: urn:nbn:se:su:diva-20605DOI: 10.1112/plms/pdm012ISI: 000249544200006OAI: diva2:187131
Available from: 2010-12-31 Created: 2007-11-28 Last updated: 2011-06-20Bibliographically approved

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