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2007-29

Intrinsic volumes and successive radii

by Henk, M., Hernández Cifre, M. A..


Series: 2007-29, Preprints

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

Abstract:
Motivated by a problem of Teissier to bound the intrinsic volumes of a convex body in terms of the inradius and the circumradius of the body, we give upper and lower bounds for the intrinsic volumes of a convex body in terms of the elementary symmetric functions of the so called successive inner and outer radii. These results improve on former bounds and, in particular, they also provide bounds for the elementary symmetric functions of the roots of Steiner polynomials in terms of the elementary symmetric functions of these radii.

Keywords:
Intrinsic volumes, inner and outer radii, roots of Steiner polynomials