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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.

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Dedicated to Prof. Dr Ludwig Danzer on the occasion of his 60th birthday

Research supported, in part, by NSF Grant DMS 8704474.

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Lutwak, E. On Quermassintegrals of mixed projection bodies. Geom Dedicata 33, 51–58 (1990). https://doi.org/10.1007/BF00147600

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