This is an announcement for the paper "No return to convexity" by Jakub Onufry Wojtaszczyk.

Abstract: In the paper we study closures of classes of log--concave measures under taking weak limits, linear transformations and tensor products. We consider what uniform measures on convex bodies can one obtain starting from some class $\mathcal{K}$. In particular we prove that if one starts from one--dimensional log--concave measures, one obtains no non--trivial uniform mesures on convex bodies. The operations we consider are easily proved to preserve a number of important properties, including a uniform bound on the isotropic constant and $IC$ inequalities.

Archive classification: math.FA math.MG math.PR

Mathematics Subject Classification: 52A23

Remarks: 12 pages

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Submitted from: onufryw@gmail.com

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http://front.math.ucdavis.edu/0910.3288

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http://arXiv.org/abs/0910.3288

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