On a loomis-whitney type inequality for permutationally invariant unconditional convex bodies

Piotr Nayar, Tomasz Tkocz

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

For a permutationally invariant unconditional convex body K in K nwe define a finite sequence (Kj)n j=1of projections of the body K to the space spanned by first j vectors of the standard basis of Rn We prove that the sequence of volumes (Kj)nj=1 is log-concave.

Original languageEnglish (US)
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar 2006-2010
PublisherSpringer Verlag
Pages327-333
Number of pages7
ISBN (Print)9783642298486
DOIs
StatePublished - 2012

Publication series

NameLecture Notes in Mathematics
Volume2050
ISSN (Print)0075-8434

Bibliographical note

Funding Information:
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. Lata?a 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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