Abstract
This paper proves that there exist 3n Steiner symmetrizations that transform any convex set K⊂ℝn into an isomorphic Euclidean ball; i.e. if vol(K)=vol(Dn) where Dn is the standard Euclidean unit ball, then K can be transformed into a body K such that c1Dn⊂K⊂c2Dn, where c1,c2 are numerical constants. Moreover, for any c>2, cn symmetrizations are also enough.
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