Abstract
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 language | English |
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Pages (from-to) | 1129-1160 |
Number of pages | 32 |
Journal | Revista Matematica Iberoamericana |
Volume | 38 |
Issue number | 4 |
Early online date | 3 Jan 2022 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Energy Optimization
- Spherical Codes
- Spherical designs
- spherical designs
- Interaction energy optimization
- spherical codes
ASJC Scopus subject areas
- Mathematics(all)