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Bounds on the roots of the Steiner polynomial
-
Madeleine Jetter
Published/Copyright:
April 8, 2011
Abstract
We consider the Steiner polynomial of a C2 convex body 
. Denote by ρmin the minimum value of the principal radii of curvature of ∂K and by ρmax their maximum. When n ≤ 5, the real parts of the roots are bounded above by –ρmin and below by –ρmax. 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.
Received: 2009-03-27
Published Online: 2011-04-08
Published in Print: 2011-April
© de Gruyter 2011
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