On the approximation of a polytope by its dual Lp-centroid bodies

Grigoris Paouris, Elisabeth M. Werner

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P ∈ Rn by its dual L p-centroid bodies is independent of the geometry of P. In particular, we show that if P has volume 1, lim p→∞ p/log p (|Z pο(P)|/|Pο|-)= n2. We provide an application to the approximation of polytopes by uniformly convex sets.

Original languageEnglish (US)
Pages (from-to)235-248
Number of pages14
JournalIndiana University Mathematics Journal
Volume62
Issue number1
DOIs
StatePublished - 2013

Keywords

  • Centroid bodies
  • Floating bodies
  • Lp Brunn Minkowski theory
  • Polytopes

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