Optimal Measures for p-frame Energies on Spheres

Ryan William Matzke, Dmitriy Bilyk, Oleksandr Vlasiuk, Josiah Park, Alexey Glazyrin

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung


We provide new answers about the distribution of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the p-frame energies, i.e., energies with the kernel given by the absolute value of the inner product raised to a positive power p. Application of linear programming methods in the setting of projective spaces allows for describing the minimizing measures in full in several cases: we show optimality of tight designs and of the 600-cell for several ranges of p in different dimensions. Our methods apply to a much broader class of potential functions, namely, those which are absolutely monotonic up to a particular order.
Seiten (von - bis)1129-1160
FachzeitschriftRevista Matematica Iberoamericana
Frühes Online-Datum3 Jan. 2022
PublikationsstatusVeröffentlicht - 2022

ASJC Scopus subject areas

  • Mathematik (insg.)


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