Packing Convex Bodies by Cylinders

Károly Bezdek, Alexander E. Litvak

Abstract: In Bezdek and Litvak (J Geom Anal 19:233–243, 2009) in relation to the unsolved Bang’s plank problem (Proc Am Math Soc 2:990–993, 1951) we obtained a lower bound for the sum of relevant measures of cylinders covering a given d-dimensional convex body. In this paper we provide the packing counterpart of these estimates. We also extend bounds to the case of r-fold covering and packing and show a packing analog of Falconer’s results (Math Proc Camb Philos Soc 87:81–96, 1980).