Stability of inequalities in the dual Brunn-Minkowski theory

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9 Citazioni (Scopus)

Abstract

Stability versions are given of several inequalities from E. Lutwak's dual Brunn-Minkowski theory. These include the dual Aleksandrov-Fenchel inequality, the dual Brunn-Minkowski inequality, and the dual isoperimetric inequality. Two methods are used. One involves the application of strong forms of Clarkson's inequality for $L^p$ norms that hold for nonnegative functions, and the other utilizes a refinement of the arithmetic-geometric mean inequality. A new and more informative proof of the equivalence of the dual Brunn-Minkowski inequality and the dual Minkowski inequality is given. The main results are shown to be the best possible up to constant factors
Lingua originaleEnglish
pagine (da-a)568-587
Numero di pagine20
RivistaJournal of Mathematical Analysis and Applications
Stato di pubblicazionePubblicato - 1999

Keywords

  • Aleksandrov-Fenchel inequality
  • Brunn-Minkowski inequality
  • Clarkson's inequality
  • dual mixed volume
  • geometric tomography
  • isoperimetric inequality
  • stability
  • star body

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