Optimal measures for p-frame energies on spheres

Authors

Dmitriy Bilyk
Alexey Glazyrin, The University of Texas Rio Grande Valley
Ryan Matzke
Josiah Park
Oleksandr Vlasiuk

Document Type

Article

Publication Date

1-3-2022

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 pp-frame energies, i.e., energies with the kernel given by the absolute value of the inner product raised to a positive power pp. 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 pp 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.

Comments

© 2022 Real Sociedad Matemática Española

Recommended Citation

Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk, Optimal measures for pp-frame energies on spheres. Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1129–1160. doi.org/10.4171/RMI/1329

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Rev. Mat. Iberoam.

DOI

10.4171/RMI/1329