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Geometry of minimizers for the interaction energy with mildly repulsive potentials

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arxiv 1607.08660 v3 pith:ODHYATD2 submitted 2016-07-28 math.AP

J. A. Carrillo , A. Figalli , F. S. Patacchini This is my paper · ORCID
classification math.AP
keywords interactionminimizersupportclassenergyglobalmildlypotentials
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abstract

We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class $C^2$ and mildly repulsive at the origin; moreover, if the minimizer is global, then its support is finite. In addition, for some class of potentials we prove the validity of a uniform upper bound on the cardinal of the support of a global minimizer. Finally, in the one-dimensional case, we give quantitative bounds.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal measures for p-frame energies on spheres

    math.MG 2019-08 accept novelty 8.0 of 10

    Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].

  2. Energy on spheres and discreteness of minimizing measures

    math.CA 2019-08 conditional novelty 7.0 of 10

    For non-even p, every minimizer of the p-frame energy on the sphere has support with empty interior, and for potentials with finitely many positive Gegenbauer coefficients a discrete minimizer always exists.

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