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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