Universal minima of potentials of certain spherical designs contained in the fewest parallel hyperplanes

2023/01/16 by Sergiy Borodachov, Borodachov, Sergiy
Mathematics · #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2301.06623

Abstract

We find the set of all universal minimum points of the potential of the 16-point sharp code on S⁴ and (more generally) of the demihypercube on S^d, d≥ 5, as well as of the 2₄₁ polytope on S⁷. We also extend known results on universal minima of three sharp configurations on S²⁰ and S²¹ containing no antipodal pair to their symmetrizations about the origin. Finally, we prove certain general properties of spherical (2m-1)-designs contained in as few as m parallel hyperplanes (all but one configuration considered here possess this property).

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