Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces. (Russian) Zbl 0648.52003
The following extremal problem is investigated. Let \(\rho\) be a measure over \({\mathbb{R}}^ n:\) find, among all (centered at the origin) oblic parallelepipeds with prescriped heights the one with a minimal \(\rho\)- volume. It is the main aim of the paper to show that, for a large class of spherically symmetric measure, a solution of this problem is to be obtained with orthogonal parallelepipeds. Applications are given to the evaluation of some characteristic invariants of convex polyhedra.
Reviewer: M.Turinici
MSC:
52A40 | Inequalities and extremum problems involving convexity in convex geometry |
28A75 | Length, area, volume, other geometric measure theory |
49Q15 | Geometric measure and integration theory, integral and normal currents in optimization |
52A20 | Convex sets in \(n\) dimensions (including convex hypersurfaces) |
52Bxx | Polytopes and polyhedra |