Majorization and minimal energy on spheres

01/13/2020

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by   Oleg R. Musin, et al.

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We consider the majorization (Karamata) inequality and minimums of the majorization (M-sets) for f-energy potentials of m-point configurations in a sphere. In particular, we show the optimality of regular simplexes, describe M-sets with a small number of points, define and discuss spherical f-designs.