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Remarks on Bourgain’s Problem on Slicing of Convex Bodies

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Geometric Aspects of Functional Analysis

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

Abstract

For a convex symmetric body K ⊂ ℝn 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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J. Lindenstrauss V. Milman

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© 1995 Birkhäuser Verlag Basel/Switzerland

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Dar, S. (1995). Remarks on Bourgain’s Problem on Slicing of Convex Bodies. In: Lindenstrauss, J., Milman, V. (eds) Geometric Aspects of Functional Analysis. Operator Theory Advances and Applications, vol 77. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9090-8_6

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  • DOI: https://doi.org/10.1007/978-3-0348-9090-8_6

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9902-4

  • Online ISBN: 978-3-0348-9090-8

  • eBook Packages: Springer Book Archive

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