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Forum Mathematicum

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On differentiability of quermassintegrals

María A. Hernández Cifre1 / Eugenia Saorín2

1Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain.

2Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain.

Citation Information: Forum Mathematicum. Volume 22, Issue 1, Pages 115–126, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/forum.2010.006, October 2009

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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.

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