Abstract
For sets of revolution B in R3, we investigate the limit distribution of minimum energy point masses on B that interact according to the logarithmic potential log(1∕r), where r is the Euclidean distance between points. We show that such limit distributions are supported only on the “outmost” portion of the surface (e.g., for a torus, only on that portion of the surface with positive curvature). Our analysis proceeds by reducing the problem to the complex plane where a nonsingular potential kernel arises, the level lines of which are ellipses.
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