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

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

2002-04-17

arxiv.org/abs/math/0204212v1

Mathematics

Functional Analysis

Scientific paper

This paper proves that for every convex body in R^n there exist 5n-4 Minkowski symmetrizations, which transform the body into an approximate Euclidean ball. This result complements the sharp c n 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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