Energy on spheres and discreteness of minimizing measures
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.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
52
References
5
Citations
NaN
KQI