Packing and covering convex bodies by cylinders

Károly Bezdek

April 5, 2016

In K. Bezdek and A. E. Litvak (J Geom Anal 19:233--243, 2009) in relation to the unsolved Bang's plank problem (Bang in 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 talk 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 (Falconer in Math Proc Camb Philos Soc 87:81--96, 1980).

This is a joint work with A. E. Litvak (Univ. of Alberta, Edmonton).