The Santaló-regions of a convex body

Meyer, Mathieu; Werner, Elisabeth

doi:10.1090/S0002-9947-98-02162-X

The Santaló-regions of a convex body
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by Mathieu Meyer and Elisabeth Werner PDF

Trans. Amer. Math. Soc. 350 (1998), 4569-4591 Request permission

Abstract:

Motivated by the Blaschke-Santaló inequality, we define for a convex body $K$ in $\mathbf {R}^n$ and for $t \in \mathbf {R}$ the Santaló-regions $S(K,t)$ of $K$. We investigate the properties of these sets and relate them to a concept of affine differential geometry, the affine surface area of $K$.

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