Sectional bodies associated with a convex body

Fradelizi, Matthieu

doi:10.1090/S0002-9939-00-05342-9

Sectional bodies associated with a convex body
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by Matthieu Fradelizi PDF

Proc. Amer. Math. Soc. 128 (2000), 2735-2744 Request permission

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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