The view-obstruction constants for \(\ell_ p\)-balls in \(\mathbb{R}^ 3\) (Q1312853)

In the view-obstruction problem, congruent closed, centrally symmetric convex bodies at the points of the grid \(({1\over 2},\dots,{1\over 2})+ \mathbb{Z}^ n\) are expanded uniformly until they intersect all \(d\)- dimensional subgroups of \(\mathbb{R}^ n\) which meet the open positive cone. If the convex body is the \(\ell_ p\)-ball in \(\mathbb{R}^ n\), the minimal blocking size is denoted by \(\upsilon_ p(n,d)\), \(d=1,\dots,n-1\). The authors determine these constants for \(1\leq p\leq\infty\), when \(n=3\) and \(d=1,2\).