The isodiametric problem with lattice-point constraints

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dc.creatorCifre, M. A. Hernandez
dc.creatorSchuermann, A.
dc.creatorVallentin, F.
dc.date2007-09-17
dc.date2007-11-14
dc.date.accessioned2026-07-07T10:05:06Z
dc.date.available2026-07-07T10:05:06Z
dc.descriptionIn 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.
dc.description12 pages, 4 figures, (v2) referee comments and suggestions incorporated, accepted in Monatshefte fuer Mathematik
dc.identifierhttps://arxiv.org/abs/0709.2587
dc.identifierhttp://arxiv.org/abs/0709.2587
dc.identifierMonatsh. Math. 155 (2008), 125-134
dc.identifierdoi:10.1007/s00605-008-0541-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169912
dc.subjectMetric Geometry
dc.subjectNumber Theory
dc.titleThe isodiametric problem with lattice-point constraints
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