Geometriae Dedicata

, Volume 171, Issue 1, pp 293–301 | Cite as

Isomorphic Steiner symmetrization of \(p\)-convex sets

Original Paper


In this paper we show that given a \(p\)-convex set \(K \subset \mathbb{R }^n\), there exist \(5n\) Steiner symmetrizations that transform it into an isomorphic Euclidean ball. That is, if \(|K| = |D_n| = \kappa _n\), we may symmetrize it, using \(5n\) Steiner symmetrizations, into a set \(K'\) such that \(c_p D_n \subset K' \subset C_p D_n\), where \(c_p\) and \(C_p\) are constants dependent on \(p\) only.


Symmetrization \(p\)-convexity Approximation by convex sets 

Mathematics Subject Classification

28A05 52A20 52A27 



The author would like to thank Prof. Vitali Milman for suggesting to extend the results in [13] to the \(p\)-convex setting, and for his useful advice and discussions. The author would also like to thank Liran Rotem and the anonymous referee for their useful comments throughout the paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Tel Aviv UniversityTel AvivIsrael

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