Optimal Measures for p-frame Energies on Spheres

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

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1129-1160
Number of pages32
JournalRevista Matematica Iberoamericana
Issue number4
Early online date3 Jan 2022
Publication statusPublished - 2022


  • Energy Optimization
  • Spherical Codes
  • Spherical designs
  • spherical designs
  • Interaction energy optimization
  • spherical codes

ASJC Scopus subject areas

  • Mathematics(all)

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