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Simplices in the Euclidean Ball

Published online by Cambridge University Press:  20 November 2018

Matthieu Fradelizi ,
Grigoris Paouris  and
Carsten Schütt
Matthieu Fradelizi
Affiliation:
Université Paris-Est Marne-la-Vallée, Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050, 77454 Marne-la-Vallée, Cedex 2, Francee-mail: matthieu.fradelizi@univ-mlv.fr
Grigoris Paouris
Affiliation:
Department of Mathematics, Texas A & M University, College Station, TX 77843, USAe-mail: grigoris paouris@yahoo.co.uk
Carsten Schütt
Affiliation:
Mathematisches Seminar, Christian Albrechts Universität, 24098 Kiel, Germanye-mail: schuett@math.uni-kiel.de
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Abstract

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We establish some inequalities for the second moment

$$\frac{1}{\left| K \right|}\,{{\int }_{K}}\left| x \right|_{2}^{2}dx$$

of a convex body $K$ under various assumptions on the position of $K$.

Keywords

52A20convex bodysimplex
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 3 , 01 September 2012 , pp. 498 - 508
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Ball, K. M., Ellipsoids of maximal volume in convex bodies. Geom. Dedicata 41(1992), 241–250.Google Scholar
[2] Böröczky, K., Böröczky, K. J., Schütt, C. and Wintsche, G., Convex bodies of minimal volume, surface area and mean width with respect to thin shells. Canad. J. Math. 60(2008), 3–32. http://dx.doi.org/10.4153/CJM-2008-001-x Google Scholar
[3] Fradelizi, M., Inégalités fonctionnelles et volume des sections des corps convexes. Thèse de Doctorat, Université Paris 6, 1998.Google Scholar
[4] Giannopoulos, A., Notes on isotropic convex bodies. Warsaw University Notes, 2003.Google Scholar
[5] Guédon, O., Sections euclidiennes des corps convexes et inégalités de concentration volumique. Thèse de Doctorat, Université Marne-la-Vallée, 1998.Google Scholar
[6] Guédon, O. and Litvak, A. E., On the symmetric average of a convex body. Adv. Geom., to appear.Google Scholar
[7] John, F., Extremum problems with inequalities as subsidiary conditions. Courant Anniversary Volume, Interscience, New York, 1948, 187–204.Google Scholar
[8] Kannan, R., Lovász, L. and Simonovits, M., Isoperimetric problems for convex bodies and a localization lemma. Discrete Comput. Geom. 13(1995), 541–559. http://dx.doi.org/10.1007/BF02574061 Google Scholar
[9] Milman, V. and Pajor, A., Isotropic positions and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space. In: Geometric aspects of functional analysis (1987–88), Lecture Notes in Math. 1376, Springer, Berlin, 1989, 64–104.Google Scholar