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Remarks on Bourgain’s Problem on Slicing of Convex Bodies

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

Abstract

For a convex symmetric body K ⊂ ℝ n we define a number L K by:
$$ nL_K^2{\left| K \right|^{2/n}} = \mathop {\min }\limits_{T \in SL(n)} \frac{1} {{\left| K \right|}} \cdot \int\limits_K {{{\left| {Tx} \right|}^2}dx\;(where\,\left| K \right| = volume\,of\,K)} $$
If the minimum is attained for T = id we say that K is in isotropic position. Any K has an affine image which is in isotropic position.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Sean Dar
    • 1
  1. 1.School of Mathematical Sciences Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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