The isodiametric problem with lattice-point constraints
Metric Geometry
2008-09-26 v2 Number Theory
Abstract
In this paper, the isodiametric problem for centrally symmetric convex bodies in the Euclidean d-space R^d containing no interior non-zero point of a lattice L is studied. It is shown that the intersection of a suitable ball with the Dirichlet-Voronoi cell of 2L is extremal, i.e., it has minimum diameter among all bodies with the same volume. It is conjectured that these sets are the only extremal bodies, which is proved for all three dimensional and several prominent lattices.
Keywords
Cite
@article{arxiv.0709.2587,
title = {The isodiametric problem with lattice-point constraints},
author = {M. A. Hernandez Cifre and A. Schuermann and F. Vallentin},
journal= {arXiv preprint arXiv:0709.2587},
year = {2008}
}
Comments
12 pages, 4 figures, (v2) referee comments and suggestions incorporated, accepted in Monatshefte fuer Mathematik