Differentiability of quermassintegrals: a classification of convex bodies. (English) Zbl 1296.52002
Part of the authors’ comprehensive program of study of inner parallel bodies and quermassintegrals, in this paper they study certain differentiability properties originating in a question of Bol. Their results have several consequences, from the decomposability of convex bodies to the behavior of the roots of Steiner polynomial. In particular, the authors prove that there exist many convex bodies in \(\mathbb{R}^n\) (\(n\geq 3\)) not satisfying the inradius condition in Teissier’s problem on the roots of Steiner polynomial.
Reviewer: Alina Stancu (Montréal)
MSC:
| 52A20 | Convex sets in \(n\) dimensions (including convex hypersurfaces) |
| 52A39 | Mixed volumes and related topics in convex geometry |
| 52A40 | Inequalities and extremum problems involving convexity in convex geometry |
Keywords:
cap body; extreme vector; form body; Hadwiger classification; inner parallel body; Steiner polynomial; tangential body; Teissier problemReferences:
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