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Inventiones mathematicae

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

Isomorphic Steiner symmetrization

  • B. KlartagEmail author
  • V.D. Milman
Article

Abstract

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.

Keywords

Unit Ball Numerical Constant Euclidean Ball Euclidean Unit Steiner Symmetrization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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