Bounds on the roots of the Steiner polynomial

2008/10/10 by Madeleine E. Jetter, Jetter, Madeleine E.
Mathematics · #52A #53C #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:52A #msc:53C

paper · pdf · doi:10.48550/arxiv.0810.1794

5 pages; corrected a typo in statement of Lemma 2.1 (Feb. 2, 2009)

arxiv created 2009/02/01 · arxiv updated 2009/12/01

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.

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