Bulletin of the Brazilian Mathematical Society, New Series

, Volume 42, Issue 1, pp 153–170

On the location of roots of Steiner polynomials

Article

DOI: 10.1007/s00574-011-0008-5

Cite this article as:
Henk, M. & Hernández Cifre, M.A. Bull Braz Math Soc, New Series (2011) 42: 153. doi:10.1007/s00574-011-0008-5

Abstract

We investigate the roots of relative Steiner polynomials of convex bodies. In dimension 3 we give a precise description of their location in the complex plane and we study the analogous problem in higher dimensions. In particular, we show that the roots (in the upper half plane) form a convex cone; for dimensions ≤ 9 this cone is completely contained in the (open) left half plane, which is not true in dimensions ≥ 12. Moreover, we characterize certain special families of convex bodies by means of properties of their roots.

Keywords

roots of Steiner polynomialtangential bodiesconstant width setssausages

Mathematical subject classification

Primary: 52A20, 52A39Secondary: 30C15

Copyright information

© Springer 2011

Authors and Affiliations

  1. 1.Fakultät für MathematikOtto-von-Guericke Universität MagdeburgMagdeburgGermany
  2. 2.Departamento de MatemáticasUniversidad de MurciaMurciaSpain