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

Research output: Contribution to journalArticle

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 - 2001

Fingerprint

Affine Invariant
Isoperimetric Inequality
Polytopes
Projection
Reverse Inequality
Convex Polytopes
Ball
Estimate

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "A new affine invariant for polytopes and schneider's projection problem",
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.",
keywords = "Affine isoperimetric inequalities, Asymptotic inequalities, Projection bodies, Reverse isoperimetric inequalities",
author = "Erwin Lutwak and Deane Yang and Gaoyong Zhang",
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journal = "Transactions of the American Mathematical Society",
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KW - Asymptotic inequalities

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KW - Reverse isoperimetric inequalities

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