Inventiones mathematicae

, Volume 153, Issue 3, pp 463–485 | Cite as

Isomorphic Steiner symmetrization

  • B. KlartagEmail author
  • V.D. Milman


This paper proves that there exist 3n Steiner symmetrizations that transform any convex set K⊂ℝ n 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 c1D n Kc2D n , where c1,c2 are numerical constants. Moreover, for any c>2, cn symmetrizations are also enough.


Unit Ball Numerical Constant Euclidean Ball Euclidean Unit Steiner Symmetrization 
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© Springer-Verlag 2003

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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