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

摘要

This paper proves that for every convex body in R^n there exist 5n-4Minkowski symmetrizations, which transform the body into an approximateEuclidean ball. This result complements the sharp c n log n upper estimate byJ. Bourgain, J. Lindenstrauss and V.D. Milman, of the number of randomMinkowski symmetrizations sufficient for approaching an approximate Euclideanball.