Packing convex bodies by cylinders
arXiv:1507.05115 · doi:10.1007/s00454-016-9760-z
Abstract
In [BL] in relation to the unsolved Bang's plank problem (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 ([Fa]).
14 pages