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Flag Measures for Convex Bodies

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Asymptotic Geometric Analysis

Part of the book series: Fields Institute Communications ((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.

Mathematical Subject Classifications (2010): 52A20, 52A22, 52A39, 53C65

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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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Authors and Affiliations

  1. Department of Mathematics, Institute of Stochastics, Karlsruhe Institute of Technology, D-76128, Karlsruhe, Germany

    Daniel Hug, Ines Türk & Wolfgang Weil

Authors
  1. Daniel Hug
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  2. Ines Türk
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  3. Wolfgang Weil
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Corresponding author

Correspondence to Daniel Hug .

Editor information

Editors and Affiliations

  1. TU Wien, Wiedner Hauptstrasse 8–10, Wien, 1040, Austria

    Monika Ludwig

  2. Fac. Exact Sciences, School of Mathematical Sciences, University of Tel Aviv, Schreiber Building 334, Tel Aviv, 69978, Israel

    Vitali D. Milman

  3. University of Ottawa, Ottawa, K1N 6N5, Canada

    Vladimir Pestov

  4. , Department of Math and Stat Scis, University of Alberta, Central Academic Bldg 632, Edmonton, T6G 2G1, Alberta, Canada

    Nicole Tomczak-Jaegermann

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Hug, D., Türk, I., Weil, W. (2013). Flag Measures for Convex Bodies. In: Ludwig, M., Milman, V., Pestov, V., Tomczak-Jaegermann, N. (eds) Asymptotic Geometric Analysis. Fields Institute Communications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6406-8_7

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