The isodiametric problem with lattice-point constraints

Details The isodiametric problem with lattice-point constraints The isodiametric problem with lattice-point constraints

2007-09-17

arxiv.org/abs/0709.2587v2

Monatsh. Math. 155 (2008), 125-134

Mathematics

Metric Geometry

12 pages, 4 figures, (v2) referee comments and suggestions incorporated, accepted in Monatshefte fuer Mathematik

Scientific paper

10.1007/s00605-008-0541-5

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.

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