Geometriae Dedicata

, Volume 33, Issue 1, pp 51–58

On Quermassintegrals of mixed projection bodies

  • Erwin Lutwak

DOI: 10.1007/BF00147600

Cite this article as:
Lutwak, E. Geom Dedicata (1990) 33: 51. doi:10.1007/BF00147600


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.

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Erwin Lutwak
    • 1
  1. 1.Department of MathematicsPolytechnic UniversityBrooklynUSA