Orlicz centroid bodies

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Abstract

The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a star body (from below) by the volume of the star body itself is the Busemann-Petty centroid inequality. A decade ago, the Lp analogue of the classical Busemann- Petty centroid inequality was proved. Here, the definition of the centroid body is extended to an Orlicz centroid body of a star body, and the corresponding analogue of the Busemann-Petty centroid inequality is established for convex bodies.

Original languageEnglish (US)
Pages (from-to)365-387
Number of pages23
JournalJournal of Differential Geometry
Volume84
Issue number2
DOIs
StatePublished - Jan 1 2010

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ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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