Energy on spheres and discreteness of minimizing measures

Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk

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7 Scopus citations


In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal measures are discrete or are supported on small sets. In particular, we prove that the support of any minimizer of the p-frame energy has empty interior whenever p is not an even integer. A similar effect is also demonstrated for energies with analytic potentials which are not positive definite. In addition, we establish the existence of discrete minimizers for a large class of energies, which includes energies with polynomial potentials.

Original languageEnglish (US)
Article number108995
JournalJournal of Functional Analysis
Issue number11
StatePublished - Jun 1 2021

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  • Potential energy minimization
  • Spherical codes
  • Spherical designs


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