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Advances in Geometry

Managing Editor: Grundhöfer, Theo

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 / Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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On the volume of inner parallel bodies

M. A. Hernández Cifre1 / E. Saorín2

1Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain. Email:

2Institut für Algebra und Geomtrie, Otto-von-Guericke Universität, Universitätsplatz 2, 39106 Magdeburg, Germany. Email:

Citation Information: Advances in Geometry. Volume 10, Issue 2, Pages 275–286, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advgeom.2010.004, March 2010

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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

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