School of Mathematical and Statistical Sciences Faculty Publications and Presentations
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.
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
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Rev. Mat. Iberoam.
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