Research problem (Q5970596)

A family \(\mathcal F\) of open plane convex subsets of \(\mathbb{R}^2\) is called a Minkowsky arrangement if the centroid of any set in \(\mathcal F\) is not contained in any other set of \(\mathcal F\). The author considers families \(\mathcal F\) of homothetic images of a fixed given open plane convex set and conjectures that the density of such a family is at most 9/2. He presents an example for such an \(\mathcal F\) the density of which is precisely equal to 9/2.