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On a Loomis–Whitney Type Inequality for Permutationally Invariant Unconditional Convex Bodies

  • Piotr NayarEmail author
  • Tomasz Tkocz
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Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)

Abstract

For a permutationally invariant unconditional convex body \(K\) in \({\mathbb{R}}^{n}\) we define a finite sequence \({({K}_{j})}_{j=1}^{n}\) of projections of the body K to the space spanned by first j vectors of the standard basis of \({\mathbb{R}}^{n}\). We prove that the sequence of volumes \({(\vert {K}_{j}\vert )}_{j=1}^{n}\) is log-concave.

Keywords

Permutation Invariance Convex Bodies Negative Correlation Property Wojtaszczyk Brunn-Minkowski Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors would like to thank Prof. K. Oleszkiewicz for a valuable comment regarding the equality conditions in Theorem 1 as well as Prof. R. Latała for a stimulating discussion. Research of the First named author partially supported by NCN Grant no. 2011/01/N/ST1/01839. Research of the second named author partially supported by NCN Grant no. 2011/01/N/ST1/05960.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WarsawWarszawaPoland

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