Mixed projection inequalities

Erwin Lutwak

Research output: Contribution to journalArticlepeer-review


A number of sharp geometric inequalities for polars of mixed projection bodies (zonoids) are obtained. Among the inequalities derived is a polar projection inequality that has the projection inequality of Petty as a spe­cial case. Other special cases of this polar projection inequality are inequalities (between the volume of a convex body and that of the polar of its 2th pro­jection body) that are strengthened forms of the classical inequalities between the volume of a convex body and its projection measures (Quermassintegrale). The relation between the Busemann-Petty centroid inequality and the Petty projection inequality is shown to be similar to the relation that exists between the Blaschke-Santalo inequality and the affine isoperimetric inequality of affine differential geometry. Some mixed integral inequalities are derived similar in spirit to inequalities obtained by Chakerian and others.

Original languageEnglish (US)
Pages (from-to)91-106
Number of pages16
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - Jan 1985


  • Centroid body
  • Convex body
  • Mixed area measure
  • Mixed volume
  • Projection measure (Quermassintegral)
  • Pro­jection body
  • Zonoid

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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