Abstract
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 language | English |
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Article number | 108995 |
Journal | Journal of Functional Analysis |
Volume | 280 |
Issue number | 11 |
DOIs | |
Publication status | Published - 1 Jun 2021 |
Keywords
- Energy Minimization
- Spherical Codes
- Spherical designs