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

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


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.


Permutation Invariance Convex Bodies Negative Correlation Property Wojtaszczyk Brunn-Minkowski Inequality 
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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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