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# Simplices in the Euclidean Ball

Published:2011-07-08
Printed: Sep 2012
Université Paris-Est Marne-la-Vallée, Laboratoire d'Analyse et de Mathématiques Appliquées, UMR 8050, 77454 Marne-la-Vallée, Cedex 2, France
• Grigoris Paouris,
Department of Mathematics, Texas A & M University, College Station, TX 77843, USA
• Carsten Schütt,
Mathematisches Seminar, Christian Albrechts Universität, 24098 Kiel, Germany
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## Abstract

We establish some inequalities for the second moment $$\frac{1}{|K|} \int_{K}|x|_2^2 \,dx$$ of a convex body $K$ under various assumptions on the position of $K$.
 Keywords: convex body, simplex
 MSC Classifications: 52A20 - Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]