Let \(D_R\), \(D_r\), \(D_S\), \(D_s\) be complex disks with common center 1 and radii R, r, S, s, respectively. We consider the Minkowski products \(A := D_R D_r\) and \(B := D_S D_s\) and give necessary and sufficient conditions for A being a subset or superset of B. Partially, this extends to n-fold disk products \(D_1\ldots D_n\), \(n>2\). 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.
complex disk products Minkowski products Cartesian ovals
Mathematics Subject Classification
Primary 53A04 Secondary 14H45
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