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Sectional bodies associated with a convex body

Abstract : We define the sectional bodies associated to a convex body in R-n and two related measures of symmetry. These definitions extend those of Grunbaum (1963). As Grunbaum conjectured, we prove that the simplices are the most dissymmetrical convex bodies with respect to these measures. In the case when the convex body has a sufficiently smooth boundary, we investigate some limit behaviours of the volume of the sectional bodies.
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Submitted on : Wednesday, May 2, 2012 - 11:53:26 PM
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Matthieu Fradelizi. Sectional bodies associated with a convex body. Proceedings of the American Mathematical Society, American Mathematical Society, 2000, 128 (9), pp.2735--2744. ⟨10.1090/S0002-9939-00-05342-9⟩. ⟨hal-00693806⟩



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