Visibility in crowds of translates of a centrally symmetric convex body

Let B p , B q be disjoint translates of a centrally symmetric convex body B in R n . A translate B r of B lies between B p and B q if it overlaps none of B p and B q and there are points x ∈ B p , y ∈ B q such that the segment [ x , y ] meets B r . For a family F of translates of B lying between B p and B q and forming a packing, these two bodies are said to be visible from each other in the system { B p , B q } ∪ F if there exist points x , y like above such that [ x , y ] intersects no translate of F ; otherwise B p and B q are concealed from each other by F . The concealment number of a Minkowski space with unit ball B is the infimum of λ > 0 with ‖ p − q ‖ > λ implying that B p , B q can be concealed from each other by translates of B . Continuing the investigations of other authors, we prove several results about concealment numbers of Minkowski planes.