Advertisement

ψ2-Estimate for the Euclidean Norm on a Convex Body in Isotropic Position

  • Simeon Alesker
Part of the Operator Theory Advances and Applications book series (OT, volume 77)

Abstract

Let ℝ n be the n-dimensional euclidean space with fixed scalar product (·,·) and the norm |x|2 = (x, x). Denote D n = {x ∈ ℝ n | |x| ≤ 1} the unit euclidean ball, |A| = vol n A the Lebesgue n-dimensional measure. Let K be compact convex body in \( \mathbb{R}^n ,b = \frac{1} {{|K|}}\int_K {xdx} \) be its centroid and \(M = (m_{ij} )_{i,j = 1}^n \) be the matrix of inertia of K with entries \( m_{ij} = \frac{1} {{|K|}}\int_K {x_i x} _j dx.\)

Keywords

Convex Body Absolute Constant Isoperimetric Problem Entry Operator Sackler Faculty 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Gr-M]
    M. Gromov, V. Milman, Brunn theorem and a concentration of volume of convex bodies, GAFA Seminar Notes, Tel Aviv University, Israel 1983–1984.Google Scholar
  2. [M-P]
    V. Milman, A. Pajor, Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, Springer LNM 1376 (1989), 64–104.MathSciNetGoogle Scholar
  3. [K-L-S]
    R. Kannan, L. Lovász, M. Simonovits, Isoperimetric problems for convex bodies and the Localization Lemma, Preprint.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Simeon Alesker
    • 1
  1. 1.Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

Personalised recommendations