A note on energy minimization in dimension 2

Abstract

Proving the universal optimality of the hexagonal lattice is one of the big open challenges of nowadays mathematics. We show that the hexagonal lattice outperforms certain "natural" classes of periodic configurations. Also, we rule out the option that the canonical non-lattice rival -- the honeycomb -- has lower energy than the hexagonal lattice at any scale.

arXiv comment13 pages, 3 figures, 21 references

References in corpus (6)

• Universally optimal distribution of points on spheres
• Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions
• Ground states and formal duality relations in the Gaussian core model
• Dimension reduction techniques for the minimization of theta functions on lattices
• Energy minimization, periodic sets and spherical designs
• Maximal Theta Functions -- Universal Optimality of the Hexagonal Lattice for Madelung-Like Lattice Energies