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Symmetrization and Isotropic Constants of Convex Bodies

Part of the Lecture Notes in Mathematics book series (LNM,volume 1850)

Abstract

We investigate the effect of a Steiner type symmetrization on the isotropic constant of a convex body. We reduce the problem of bounding the isotropic constant of an arbitrary convex body, to the problem of bounding the isotropic constant of a finite volume ratio body. We also add two observations concerning the slicing problem. The first is the equivalence of the problem to a reverse Brunn-Minkowski inequality in isotropic position. The second is the essential monotonicity in n of where the supremum is taken over all convex bodies in , and L K is the isotropic constant of K.

Mathematics Subject Classification (2000):

  • 46-06
  • 46B07
  • 52-06 60-06

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Correspondence to J. Bourgain .

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© 2004 Springer-Verlag Berlin/Heidelberg

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Bourgain, J., Klartag, B., Milman, V. (2004). Symmetrization and Isotropic Constants of Convex Bodies. In: Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44489-3_10

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  • DOI: https://doi.org/10.1007/978-3-540-44489-3_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22360-3

  • Online ISBN: 978-3-540-44489-3

  • eBook Packages: Springer Book Archive