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Nondegeneracy of certain constrained extrema

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Abstract

The isolation and nondegeneracy of constrained extrema arising in geometric problems and mathematical models of electrostatics are studied. In particular, it is proved that a convex concyclic configuration of polygonal linkages is a nondegenerate maximum of the oriented area. Geometric properties of equilibrium configurations of point charges with Coulomb interaction on convex curves are considered, and methods for constructing them are presented. It is shown that any configuration of an odd number of points on a circle is an equilibrium point for the Coulomb potential of nonzero point charges. The stability of the equilibrium configurations under consideration is discussed.

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Authors and Affiliations

  1. Javakhishvili Tbilisi State University, Universitetskaya ul. 1, Tbilisi, 0186, Georgia

    G. K. Giorgadze

  2. Ilia State University, pr. Cholokashvili 3/5, Tbilisi, 0162, Georgia

    G. N. Khimshiashvili

Authors
  1. G. K. Giorgadze
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  2. G. N. Khimshiashvili
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Correspondence to G. K. Giorgadze.

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Original Russian Text © G.K. Giorgadze, G.N. Khimshiashvili, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 3, pp. 269–273.

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Giorgadze, G.K., Khimshiashvili, G.N. Nondegeneracy of certain constrained extrema. Dokl. Math. 92, 691–694 (2015). https://doi.org/10.1134/S1064562415060149

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  • DOI: https://doi.org/10.1134/S1064562415060149

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