A note on energy minimization in dimension 2
Classical Analysis and ODEs
2024-12-24 v1 Mathematical Physics
Metric Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.2306.16266,
title = {A note on energy minimization in dimension 2},
author = {Markus Faulhuber and Irina Shafkulovska and Ilia Zlotnikov},
journal= {arXiv preprint arXiv:2306.16266},
year = {2024}
}
Comments
13 pages, 3 figures, 21 references