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5n Minkowski Symmetrizations Suffice to Arrive at an Approximate Euclidean Ball

B. Klartag
Annals of Mathematics
Second Series, Vol. 156, No. 3 (Nov., 2002), pp. 947-960
Published by: Annals of Mathematics
DOI: 10.2307/3597288
Stable URL: http://www.jstor.org/stable/3597288
Page Count: 14
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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.

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