Optimal measures for $p$-frame energies on spheres

@article{Bilyk2022OptimalMF,
  title={Optimal measures for \$p\$-frame energies on spheres},
  author={Dmitriy Bilyk and Alexey A. Glazyrin and Ryan Matzke and Josiah Park and O. V. Vlasiuk},
  journal={Revista Matem{\'a}tica Iberoamericana},
  year={2022}
}
We provide new answers about the placement 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… 

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