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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: 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 10, Issue 2 (Jan 2010)


On the volume of inner parallel bodies

M. A. Hernández Cifre
  • Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain. Email:
  • Other articles by this author:
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/ E. Saorín
  • Institut für Algebra und Geomtrie, Otto-von-Guericke Universität, Universitätsplatz 2, 39106 Magdeburg, Germany. Email:
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Published Online: 2010-03-10 | DOI: https://doi.org/10.1515/advgeom.2010.004


Motivated by a conjecture of Matheron, we provide bounds for the volume of the inner parallel body of a convex body K involving the alternating Steiner polynomial of K. As a consequence we get that this conjecture is not true since, in fact, we prove it is not possible to bound the volume of the inner parallel body in terms of just the alternating Steiner polynomial itself.

Key words.: Inner parallel body; volume; quermassintegrals; alternating Steiner polynomial; tangential bodies

About the article

Received: 2007-12-04

Published Online: 2010-03-10

Published in Print: 2010-04-01

Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.004.

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