Zurück zu den Preprints des Jahres 2010


How to make quermassintegrals differentiable: solving a problem by Hadwiger

by Hernández Cifre, M. A., Saorín Gómez, E..

Series: 2010-28, Preprints

52A20 Convex sets in $n$ dimensions (including convex hypersurfaces)
52A39 Mixed volumes and related topics
52A40 Inequalities and extremum problems

In this paper we characterize the convex bodies in R^n whose
quermassintegrals satisfy certain differentiability properties, which fully
solves a problem posed by Hadwiger in R^3. This result will have unexpected consequences on the behavior of the roots of the Steiner polynomial: we prove that there exist many convex bodies in R^n, for any n>=3, not satisfying Teissier's problem on the geometric properties of the roots of the Steiner polynomial related to the inradius of the set.

Hadwiger problem, inner parallel body, Steiner polynomial, Teissier problem, inradius, quermassintegrals, tangential body, extreme vector, form body.