Optimal Antipodal Configuration of 2d Points on a Sphere in \mathbb R^d for Covering

2022/10/22 by Borodachov, Sergiy
#52A20 #52B05 #52B10 #52B12 #52C17 #FOS: Mathematics #Optimization and Control (math.OC) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2210.12472

Abstract

We show that among antipodal 2d-point configurations on the sphere S^d-1 in \mathbb R^d, the set of vertices of a regular cross-polytope inscribed in S^d-1 uniquely solves the best-covering problem (this is new for d≥ 5) and the maximal polarization problem for potentials given by a function of the distance squared with a positive and convex second derivative (d≥ 3).

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