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 | References | Similar Articles | Additional Information

We define the sectional bodies associated to a convex body in 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