On the density of dual circle coverings
Let C be a family of distinct unit circles in the Euclidean plane. The dual of the family C is the collection \(C^*\) of all unit circles which are centered at points belonging to the boundary of at least two members of C. If C is a covering of the plane, then so is \(C^*\). Let \(d^-(C)\) denote the lower density of the family C. The main theorem states that \(d^-(C)\leq d^-(C^*)\) for any covering C by unit circles. \textit{K. Bezdek} and \textit{R. Connelly} [Ann. Univ. Sci. Budapest Rolando Eötvös, Sect. Math. 31, 115-127 (1988; Zbl 0683.52014)] have proved this inequality for such coverings C which contain no pair of tangent circles.
scientific article; zbMATH DE number 4146977