The Fermat–Steiner problem in the space of compact subsets of the Euclidean plane

The Fermat–Steiner problem if the problem of finding all points of a metric space $Y$ such that the sum of the distances from them to points of a certain fixed finite subset $A$ of the space $Y$ is minimal. In this paper, we examine the Fermat–Steiner problem in the case where $Y$ is the space of compact subsets of the Euclidean plane endowed with the Hausdorff metric, and points of $A$ are finite pairwise disjoint compact sets.