Article contents
Simplices in the Euclidean Ball
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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
- Type
- Research Article
- Information
- 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
- 2
- Cited by