, Volume 33, Issue 1, pp 51-58

On Quermassintegrals of mixed projection bodies

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Abstract

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.

Dedicated to Prof. Dr Ludwig Danzer on the occasion of his 60th birthday
Research supported, in part, by NSF Grant DMS 8704474.