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Flag Measures for Convex Bodies

  • Daniel Hug
  • Ines Türk
  • Wolfgang Weil
Chapter
Part of the Fields Institute Communications book series (FIC, volume 68)

Abstract

Measures on flag manifolds have been recently used to describe local properties of convex bodies and more general sets in \({\mathbb{R}}^{d}\). Here, we provide a systematic account of flag measures for convex bodies, we collect various properties of flag measures and we prove some new results. In particular, we discuss mixed flag measures for several bodies and we present formulas for (mixed) flag measures of generalized zonoids.

Key words

Support measure Mixed area measure Flag support measure Grassmannian Integral geometry Zonoids 

Notes

Acknowledgements

The authors are grateful for support from the German Science Foundation (DFG) and the Czech Science Foundation (GAČR 201/10/J039) for the joint project “Curvature Measures and Integral Geometry”. The first and the third named author gratefully acknowledge support from the Fields Institute.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsInstitute of Stochastics, Karlsruhe Institute of TechnologyKarlsruheGermany

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