Bounds on the roots of the Steiner polynomial

2008/10/10 by Madeleine E. Jetter, Jetter, Madeleine E.
Biochemistry, Genetics and Molecular Biology · Mathematics · #52A #53C #Boundary (topology) #Bounded function #Combinatorics #Curvature #Diffusion and Search Dynamics #Discrete mathematics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Mathematical analysis #Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Polynomial #Regular polygon #Steiner tree problem #Value (mathematics) #math.MG #msc:52A #msc:53C

paper · pdf · doi:10.48550/arxiv.0810.1794

published in arXiv (Cornell University) (Cornell University) · 5 pages; corrected a typo in statement of Lemma 2.1 (Feb. 2, 2009)

openalex publication_date 2008/10/10 · arxiv created 2009/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the Steiner polynomial of a C² convex body K in Rⁿ (n ≤ 5). The opposites of the real parts of the roots of the Steiner polynomial are bounded below by the minimum value and above by the maximum value of the principal radii of curvature of the boundary of K.

Citations

• Notes on the roots of Steiner polynomials

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