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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On the volume of inner parallel bodies
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.
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