This is an announcement for the paper "Rotation equivariant Minkowski valuations" by Rolf Schneider and Franz E. Schuster.

Abstract: The projection body operator \Pi, which associates with every convex body in Euclidean space Rn its projection body, is a continuous valuation, it is invariant under translations and equivariant under rotations. It is also well known that \Pi\ maps the set of polytopes in Rn into itself. We show that \Pi\ is the only non-trivial operator with these properties.

Archive classification: math.MG math.DG math.FA

Mathematics Subject Classification: 52A20, 52B11, 52B45

Citation: Int. Math. Res. Not. 2006, Art. ID 72894, 20 pp

Submitted from: franz.schuster@tuwien.ac.at

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.7279

or

http://arXiv.org/abs/1207.7279