A new affine invariant for polytopes and schneider's projection problem

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Abstract

New affine invariant functionals for convex polytopes are introduced. Some sharp affine isoperimetric inequalities are established for the new functionals. These'new inequalities lead to fairly strong volume estimates for projection bodies. Two of the new affine isoperimetric inequalities are extensions of Ball's reverse isoperimetric inequalities.

Original languageEnglish (US)
Pages (from-to)1767-1779
Number of pages13
JournalTransactions of the American Mathematical Society
Volume353
Issue number5
StatePublished - Dec 1 2001

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Keywords

  • Affine isoperimetric inequalities
  • Asymptotic inequalities
  • Projection bodies
  • Reverse isoperimetric inequalities

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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