A general isepiphanic inequality

Erwin Lutwak

Research output: Contribution to journalArticlepeer-review


An inequality of Petty regarding the volume of a convex body and that of the polar of its projection body is shown to lead to an inequality between the volume of a convex body and the power means of its brightnees function. A special case of this power-mean inequality is the classical isepiphanic (isoperimetric) inequality. The power-mean inequality can also be used to obtain strengthened forms and extensions of some known and conjectured geometric inequalities. Affine projection measures (Quermassintegrale) are introduced.

Original languageEnglish (US)
Pages (from-to)415-421
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Mar 1984


  • Convex body
  • Projection body
  • Projection measure (Quermassintegrale)

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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