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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Strambach, Karl

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Joswig, Michael / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Penttila, Tim / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Sommese, Andrew J. / Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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

Citation Information: Advances in Geometry. Volume 7, Issue 2, Pages 275–294, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/ADVGEOM.2007.016, June 2007

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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

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