Energy on spheres and discreteness of minimizing measures
| Autor: | Oleksandr Vlasiuk, Dmitriy Bilyk, Josiah Park, Ryan Matzke, Alexey Glazyrin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Polynomial
010102 general mathematics Mathematical analysis FOS: Physical sciences Metric Geometry (math.MG) Mathematical Physics (math-ph) Positive-definite matrix 01 natural sciences Integer Mathematics - Metric Geometry 52A40 31E05 58C35 90C26 Mathematics - Classical Analysis and ODEs 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics SPHERES 010307 mathematical physics Minification 0101 mathematics Focus (optics) Cluster analysis Analysis Energy (signal processing) Mathematical Physics Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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