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Sectional bodies associated with a convex body |
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| Authors: | Matthieu Fradelizi |
| Institution: | Université de Marne-la-Vallée, Equipe d'Analyse et de Mathématiques Appliquées, Cité Descartes, 5 Bd Descartes, Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France |
| Abstract: | We define the sectional bodies associated to a convex body in |
| Keywords: | Gaussian curvature affine surface area measure of symmetry |
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and two related measures of symmetry. These definitions extend those of Grünbaum (1963). As Grünbaum 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.