Generalizations of the Busemann-Petty problem for sections of convex bodies

Boris Rubin, Gaoyong Zhang

Research output: Contribution to journalArticle

Abstract

We present generalizations of the Busemann-Petty problem for dual volumes of intermediate central sections of symmetric convex bodies. It is proved that the answer is negative when the dimension of the sections is greater than or equal to 4. For two- three-dimensional sections, both negative and positive answers are given depending on the orders of dual volumes involved, and certain cases remain open. For bodies of revolution, a complete solution is obtained in all dimensions.

Original languageEnglish (US)
Pages (from-to)473-501
Number of pages29
JournalJournal of Functional Analysis
Volume213
Issue number2
DOIs
StatePublished - Aug 15 2004

Keywords

  • Convex bodies
  • Dual volumes
  • The Busemann-Petty problem
  • The spherical Radon transform

ASJC Scopus subject areas

  • Analysis

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