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On the roots of the Steiner polynomial of a 3-dimensional convex body
-
M. A Hernández Cifre
and
E Saorín
Published/Copyright:
June 18, 2007
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
Received: 2006-03-30
Revised: 2006-07-14
Published Online: 2007-06-18
Published in Print: 2007-04-19
© Walter de Gruyter
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Keywords for this article
Roots of the Steiner polynomial;
Blaschke's problem;
Teissier's conjecture;
volume;
surface area;
integral mean curvature;
circumradius;
inradius
Articles in the same Issue
- The Poncelet grid
- On hyperbolic Coxeter n-polytopes with n + 2 facets
- Dense near octagons with four points on each line, II
- On the Hermitian curvature of symplectic manifolds
- Surjectivity of Gaussian maps for curves on Enriques surfaces
- Compact Tits quadrangles as Lie geometries of topological Laguerre spaces
- On the roots of the Steiner polynomial of a 3-dimensional convex body
- Circular surfaces
- Addendum to “Classification of generalized polarized manifolds by their nef values”
