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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Santaló-regions of a convex body

Authors: Mathieu Meyer and Elisabeth Werner
Journal: Trans. Amer. Math. Soc. 350 (1998), 4569-4591
MSC (1991): Primary 52A20; Secondary 52A38
MathSciNet review: 1466952
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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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Mathieu Meyer
Affiliation: Université de Marne-La-Valee, Equipe d’Analyse et de Mathématiques Appliquees, Cité Descartes-5, bd Descartes-Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France

Elisabeth Werner
Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
Address at time of publication: Université de Lille 1, UFR de Mathématiques, 59655 Villeneuve d’Ascq, France

Keywords: Blaschke-Santaló inequality, affine surface area
Received by editor(s): October 25, 1996
Additional Notes: Supported by a grant from the National Science Foundation
The paper was written while both authors were at MSRI
Article copyright: © Copyright 1998 American Mathematical Society