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On differentiability of quermassintegrals
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María A. Hernández Cifre
Published/Copyright:
October 5, 2009
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
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Articles in the same Issue
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- Curvature of almost quaternion-Hermitian manifolds
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- No invariant line fields on Cantor Julia sets
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- The number of configurations in lattice point counting I
- On the Fourier coefficients of modular forms of half-integral weight
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