On Monotone Translation–Projection Covariant Minkowski Valuations
We study Minkowski valuations compatible with translations and projections. We first introduce the concept of translation–projection covariance for Minkowski valuations. Then, we show that, under some conditions, monotone translation–projection covariant Minkowski valuations are exactly orthogonal projections, which gives a characterization of the orthogonal projection operators on Euclidean spaces.
KeywordsMinkowski valuation Orthogonal projection Translation Covariance Convex body
Mathematics Subject Classification52A20 52B45
The authors express sincere thanks to the reviewers for their careful reading the first and the second versions of this paper, pointing out some language errors and for their valuable suggestions and comments which improved the paper.
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