Energy on spheres and discreteness of minimizing measures

Authors

Dmitriy Bilyk
Alexey Glazyrin, The University of Texas Rio Grande Valley
Ryan Matzke
Josiah Park
Oleksandr Vlasiuk

Document Type

Article

Publication Date

6-1-2021

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.

Comments

Original published version available at https://doi.org/10.1016/j.jfa.2021.108995

Recommended Citation

Bilyk, Dmitriy, Alexey Glazyrin, Ryan Matzke, Josiah Park, and Oleksandr Vlasiuk. "Energy on spheres and discreteness of minimizing measures." Journal of Functional Analysis 280, no. 11 (2021): 108995. https://doi.org/10.1016/j.jfa.2021.108995

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Journal of Functional Analysis

DOI

10.1016/j.jfa.2021.108995