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M. A Hernndez Cifre, E Saorn

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

Keywords: Roots of the Steiner polynomial, volume, surface area, integral mean curvature, circumradius, inradius

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.

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 7, 04/2007
Pages: 275 - 294

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