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

### Abstract

For a permutationally invariant unconditional convex body K in 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 R^n. We prove that the sequence of volumes (|K_1|, ..., |K_n|) is log-concave.Comment: 6 page

Topics: Mathematics - Functional Analysis, 52A20 (Primary), 52A40 (Secondary)
Year: 2012
OAI identifier: oai:arXiv.org:1103.6232