Isomorphic Steiner symmetrization

B. Klartag*, V. D. Milman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 K̃ such that c1Dn ⊂ K̃ ⊂ c2D n, where c1, c2 are numerical constants. Moreover, for any c > 2, cn symmetrizations are also enough.

Original languageEnglish
Pages (from-to)463-485
Number of pages23
JournalInventiones Mathematicae
Issue number3
StatePublished - 2003


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