Strict Periodic Extreme Lattices
Metric Geometry
2014-06-23 v1 Number Theory
Abstract
A lattice is called periodic extreme if it cannot locally be modified to yield a better periodic sphere packing. It is called strict periodic extreme if its sphere packing density is an isolated local optimum among periodic point sets. In this note we show that a lattice is periodic extreme if and only if it is extreme, that is, locally optimal among lattices. Moreover, we show that a lattice is strict periodic extreme if and only if it is extreme and non-floating.
Keywords
Cite
@article{arxiv.1211.5534,
title = {Strict Periodic Extreme Lattices},
author = {Achill Schürmann},
journal= {arXiv preprint arXiv:1211.5534},
year = {2014}
}
Comments
6 pages; to appear in AMS Contemporary Mathematics issue on "Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms", edited by Wai Kiu Chan, Lenny Fukshansky, Rainer Schulze-Pillot, and Jeff Vaaler