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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

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

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Volume 7, Issue 2 (Apr 2007)

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

M. A Hernández Cifre
  • Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain.
  • Email:
/ E Saorín
  • Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain.
  • Email:
Published Online: 2007-06-18 | DOI: https://doi.org/10.1515/ADVGEOM.2007.016

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

About the article


Received: 2006-03-30

Revised: 2006-07-14

Published Online: 2007-06-18

Published in Print: 2007-04-19


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/ADVGEOM.2007.016.

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Citing Articles

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[1]
María A. Hernández Cifre and Jesús Yepes Nicolás
Journal of Mathematical Analysis and Applications, 2013, Volume 401, Number 2, Page 733
[2]
Martin Henk and María A. Hernández Cifre
Journal of Mathematical Analysis and Applications, 2008, Volume 343, Number 2, Page 733
[3]
María A. Hernández Cifre and Eugenia Saorín
Forum Mathematicum, 2010, Volume 22, Number 1
[4]
Martin Henk and María A. Hernández Cifre
Bulletin of the Brazilian Mathematical Society, New Series, 2011, Volume 42, Number 1, Page 153

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