A Family of Universally Optimal Configurations on Rectangular Flat Tori

2023/11/09 by Tenpas, Nathaniel
#52C35 #74G65 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.05594

Abstract

We utilize recently introduced linear programming bounds for the energy of periodic configurations in ℝ^d to construct configurations which are universally optimal among those of the form ω₄+L_β, where ω₄ is a 4-point multiset and L_β⊆ ℝ² is a rectangular lattice. For two values of the parameter β, the configurations are obtained from the A₂ lattice. Other values of β yield the third, and largest cardinality, class of examples of Λ-universally optimal configurations which do not arise from lattices Λ known or conjectured to be universally optimal in ℝ^d.

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