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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / 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 / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 11, Issue 2


Bounds on the roots of the Steiner polynomial

Madeleine Jetter
  • Department of Mathematics, California State University, San Bernardino, 5500 University Parkway, San Bernardino, CA 92407, USA
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Published Online: 2011-04-08 | DOI: https://doi.org/10.1515/advgeom.2011.008


We consider the Steiner polynomial of a C 2 convex body . Denote by ρ min the minimum value of the principal radii of curvature of ∂K and by ρ max their maximum. When n ≤ 5, the real parts of the roots are bounded above by –ρ min and below by –ρ max. These bounds are valid for any n such that all of the roots of the Steiner polynomial of every convex body in lie in the left half-plane.

About the article

Received: 2009-03-27

Published Online: 2011-04-08

Published in Print: 2011-04-01

Citation Information: Advances in Geometry, Volume 11, Issue 2, Pages 313–317, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2011.008.

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