Covering Convex Bodies by Cylinders and Lattice Points by Flats

被引：0
|
作者：
K. Bezdek
A. E. Litvak
机构：
[1] University of Calgary,Department of Mathematics and Statistics
[2] University of Alberta,Department of Mathematical and Statistical Sciences
来源：
Journal of Geometric Analysis | 2009年 / 19卷
关键词：
Convex body; Banach-Mazur distance; Covering by cylinders; Covering lattice points by flats; 52A40; 52C07; 46B07; 46B20; 52C17;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In connection with an unsolved problem of Bang (1951) we give a lower bound for the sum of the base volumes of cylinders covering a d-dimensional convex body in terms of the relevant basic measures of the given convex body. As an application we establish lower bounds on the number of k-dimensional flats (i.e. translates of k-dimensional linear subspaces) needed to cover all the integer points of a given convex body in d-dimensional Euclidean space for 1≤k≤d−1.
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页码：233 / 243
页数：10
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