On the roots of the Steiner polynomial of a 3-dimensional convex body

M. A Hernández Cifre; E Saorín

doi:10.1515/ADVGEOM.2007.016

Published by De Gruyter June 18, 2007

On the roots of the Steiner polynomial of a 3-dimensional convex body

M. A Hernández Cifre and E Saorín

From the journal Advances in Geometry

https://doi.org/10.1515/ADVGEOM.2007.016

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Abstract

In this paper we study the geometric meaning of the roots of the Steiner polynomial in the 3-dimensional space. We give a complete characterization of the convex bodies in ℝ³ depending on the type of roots of their Steiner polynomials. Furthermore, we show that these roots are also related to the famous Blaschke problem and the Teissier conjecture.

Key words: Roots of the Steiner polynomial; Blaschke's problem; Teissier's conjecture; volume; surface area; integral mean curvature; circumradius; inradius

(Communicated by G. M. Ziegler)

Received: 2006-03-30

Revised: 2006-07-14

Published Online: 2007-06-18

Published in Print: 2007-04-19

On the roots of the Steiner polynomial of a 3-dimensional convex body

Abstract

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