On the (Dual) Blaschke diagram
The relation between properties of the roots of Steiner polynomials and the Blaschke diagram is investigated. The behavior of the roots of the Steiner polynomial of a~convex body embedded in a higher dimensional space is studied. In the 3-dimensional case, the involved sets follow a precise pattern when they are mapped into the Blaschke diagram. The so-called dual Blaschke diagram is constructed and characterized. As an immediate consequence, a new characterization of dual quermassintegrals in dimension \(n = 3\) is put forward. The corresponding Blaschke problem in the setting of the so-called dual Brunn-Minkowski theory is studied.
scientific article; zbMATH DE number 7371772
scientific article