标题： 具有格点约束的等直径问题 显示英文标题

标题： The isodiametric problem with lattice-point constraints

摘要： 在本文中，研究了包含格点L无内部非零点的欧几里得d维空间R^d中的中心对称凸体的等直径问题。 展示了适当球体与2L的Dirichlet-Voronoi单元的交集是极值的，即在所有具有相同体积的体中，它具有最小直径。 猜想这些集合是唯一的极值体，这一猜想已对于所有三维情况和几个显著的格点得到证明。 显示英文摘要

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.