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On Monotone Translation–Projection Covariant Minkowski Valuations

  • Yun Xu
  • Qi GuoEmail author
Article

Abstract

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.

Keywords

Minkowski valuation Orthogonal projection Translation Covariance Convex body 

Mathematics Subject Classification

52A20 52B45 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSuzhou University of Science and TechnologySuzhouChina

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