Let DR, Dr, DS, Ds be complex disks with common center 1 and radii R, r, S, s, respectively. We consider the Minkowski products A: = DRDr and B: = DSDs and give necessary and sufficient conditions for A being a subset or superset of B. Partially, this extends to n-fold disk products D1… Dn, n> 2. It is well-known that the boundaries of A and B are outer loops of Cartesian ovals. Therefore, our results translate to necessary and sufficient conditions under which such loops encircle each other.
