5n Minkowski symmetrizations suffice to arrive at an approximate Euclidean ball

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Abstract

This paper proves that for every convex body in ℝn there exist 5n Minkowski symmetrizations which transform the body into an approximate Euclidean ball. This result complements the sharp cn log n upper estimate by J. Bourgain, J. Lindenstrauss and V.D. Milman, of the number of random Minkowski symmetrizations sufficient for approaching an approximate Euclidean ball.

Original languageEnglish
Pages (from-to)947-960
Number of pages14
JournalAnnals of Mathematics
Volume156
Issue number3
DOIs
StatePublished - Nov 2002

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