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Isomorphic Steiner symmetrization

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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(D n ) where D n is the standard Euclidean unit ball, then K can be transformed into a body K such that c 1 D n Kc 2 D n , where c 1,c 2 are numerical constants. Moreover, for any c>2, cn symmetrizations are also enough.

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Klartag, B., Milman, V. Isomorphic Steiner symmetrization. Invent. math. 153, 463–485 (2003). https://doi.org/10.1007/s00222-003-0290-y

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