Visibility in crowds of translates of a centrally symmetric convex body

AbstractLet Bp, Bq be disjoint translates of a centrally symmetric convex body B in Rn. A translate Br of B lies between Bp and Bq if it overlaps none of Bp and Bq and there are points x∈Bp, y∈Bq such that the segment [x,y] meets Br. For a family F of translates of B lying between Bp and Bq and forming a packing, these two bodies are said to be visible from each other in the system {Bp,Bq}∪F if there exist points x,y like above such that [x,y] intersects no translate of F; otherwise Bp and Bq 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 Bp,Bq 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