Rotation equivariant Minkowski valuations
Metric Geometry
2012-08-01 v1 Differential Geometry
Functional Analysis
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.
Cite
@article{arxiv.1207.7279,
title = {Rotation equivariant Minkowski valuations},
author = {Rolf Schneider and Franz E. Schuster},
journal= {arXiv preprint arXiv:1207.7279},
year = {2012}
}