The isodiametric problem with lattice-point constraints

被引：0
|
作者：
Hernandez Cifre, M. A. [1 ]
Schuermann, A. [2 ]
Vallentin, F. [3 ]
机构：
[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain
[2] Otto von Guericke Univ Magdegurg, D-39106 Magdeburg, Germany
[3] Ctr Wiskunde & Informat, NL-1098 SJ Amsterdam, Netherlands
来源：
MONATSHEFTE FUR MATHEMATIK | 2008年 / 155卷 / 02期
关键词：
isodiametric problem; lattices; Dirichlet-Voronoi cells; parallelohedra;
D O I：
10.1007/s00605-008-0541-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：125 / 134
页数：10
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