Geometriae Dedicata

, Volume 184, Issue 1, pp 115–119 | Cite as

Minkowski symmetrizations of star shaped sets

Original Paper


We provide sharp upper bounds for the number of symmetrizations required to transform a star shaped set in \({\mathbb {R}}^n\) arbitrarily close (in the Hausdorff metric) to the Euclidean ball.


Symmetrization Minkowski Star shaped sets Convergence rate 

Mathematics Subject Classification

52A30 52A20 52A23 52A27 


  1. 1.
    Bourgain, J., Lindenstrauss, J., Milman, V.D.: Minkowski sums and symmetrizations. In: Lindenstrauss, J., Milman, V.D. (eds.) Geometric Aspects of Functional Analysis-Israel Seminar (1986–87),Vol. 1317, pp. 44–66. Springer, Heidelberg (1988)Google Scholar
  2. 2.
    Klartag, B.: Rate of convergence of geometric symmetrization. Geom. Funct. Anal. (GAFA) 14(6), 1322–1338 (2004)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.School of Mathematical ScienceTel Aviv UniversityTel AvivIsrael

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