Diethard Pallaschke Pairs of compact convex sets

• 2 stele, bazat pe 1 voturi

Pairs of compact convex sets arise in the quasidifferential calculus of V.

Demyanov and A.

Rubinov as sub- and superdifferentials of quasidifferen- tiable functions (see [26]) and in the formulas for the numerical evaluation of the Aumann-Integral which were recently introduced in a series of papers by R.

Baier and F.

Lempio (see [4], [5], [10] and [9]) and R.

Baier and E.

Farkhi [6], [7], [8].

In the field of combinatorial convexity G.

Ewald et al.

[36] used an interesting construction called virtual polytope, which can also be represented as a pair of polytopes for the calculation of the combinatorial Picard group of a fan.

Since in all mentioned cases the pairs of compact con- vex sets are not uniquely determined, minimal representations are of special to the existence of minimal pairs of compact importance.

A problem related convex sets is the existence of reduced pairs of convex bodies, which has been studied by Chr.

Bauer (see [14]).