Centroid bodies and the logarithmic Laplace transform - A unified approach

Bo'az Klartag, Emanuel Milman

Research output: Contribution to journalArticlepeer-review

Abstract

We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's ψ2 constant is obtained. Along the way, we present some new bounds on the volume of Lp-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the Lp-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author.

Original languageEnglish
Pages (from-to)10-34
Number of pages25
JournalJournal of Functional Analysis
Volume262
Issue number1
DOIs
StatePublished - 1 Jan 2012

Keywords

  • Hyperplane conjecture
  • Logarithmic Laplace transform
  • Psi-2

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