School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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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.


© 2022 Real Sociedad Matemática Española

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

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Rev. Mat. Iberoam.



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Mathematics Commons



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