On Quermassintegrals of mixed projection bodies

Erwin Lutwak

Research output: Contribution to journalArticlepeer-review


One of the major outstanding questions in Geometric Convexity is Petty's conjectured inequality between the volume of a convex body and that of its projection body. It is shown that if Petty's conjectured inequality holds, then it is the first of a family of such inequalities (involving mixed projection bodies). All of the members of this family are strengthened versions of the classical inequalities between pairs of Quermassintegrals of a convex body. The last member of this family (of conjectured inequalities) is established.

Original languageEnglish (US)
Pages (from-to)51-58
Number of pages8
JournalGeometriae Dedicata
Issue number1
StatePublished - Jan 1990

ASJC Scopus subject areas

  • Geometry and Topology


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