Covering convex bodies by cylinders and lattice points by flats

Details Covering convex bodies by cylinders and lattice points by flats Covering convex bodies by cylinders and lattice points by flats

2009-03-27

arxiv.org/abs/0903.4842v1

J. Geom. Anal. 19/2 (2009), 233-243

Mathematics

Metric Geometry

Scientific paper

10.1007/s12220-008-9063-6

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 0

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