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Sectional bodies associated with a convex body


Author: Matthieu Fradelizi
Journal: Proc. Amer. Math. Soc. 128 (2000), 2735-2744
MSC (2000): Primary 52A20, 52A40, 53A05, 53A15
DOI: https://doi.org/10.1090/S0002-9939-00-05342-9
Published electronically: February 28, 2000
MathSciNet review: 1664362
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Abstract:

We define the sectional bodies associated to a convex body in $\mathbb{R}^n$ 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.


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Additional Information

Matthieu Fradelizi
Affiliation: 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
Email: fradeliz@math.univ-mlv.fr

DOI: https://doi.org/10.1090/S0002-9939-00-05342-9
Keywords: Gaussian curvature, affine surface area, measure of symmetry
Received by editor(s): May 11, 1998
Received by editor(s) in revised form: October 29, 1998
Published electronically: February 28, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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