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Abstract
In this paper we study the problem of classifying the convex bodies in , depending on the differentiability of their associated quermassintegrals with respect to the one-parameter-depending family given by the inner and outer parallel bodies. This problem was originally posed by Hadwiger in the 3-dimensional space. We characterize one of the non-trivial classes and give necessary conditions for a convex body to belong to the others. We also consider particular families of convex bodies, e.g. polytopes and tangential bodies.
Received: 2008-02-14
Published Online: 2009-10-05
Published in Print: 2010-January
© de Gruyter 2010