Minimal pairs in classes of frustums (Q2733916)

On the set of pairs of non-empty compact convex subsets of a topological vector space the author considers the partial order: \((A,B)\leq (C,D)\) if \(A\subset C\), \(B\subset D\), and \(A+D=B+C\). A frustum is the convex hull of two compact convex sets lying in two different parallel hyperplanes. NEWLINENEWLINENEWLINEGiven a pair \((F,G)\) of frustums the author presents several methods for producing a pair of frustums \((F',G')\leq (F,G)\) and finds conditions under which the pair \((F',G')\) is minimal.