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Geometric & Functional Analysis GAFA

, Volume 14, Issue 6, pp 1322–1338 | Cite as

Rate of convergence of geometric symmetrizations

  • B. KlartagEmail author
Original Paper

Abstract.

It is a classical fact, that given an arbitrary convex body \(K \subset \mathbb{R}^n ,\) there exists an appropriate sequence of Minkowski symmetrizations (or Steiner symmetrizations), that converges in Hausdorff metric to a Euclidean ball. Here we provide quantitative estimates regarding this convergence, for both Minkowski and Steiner symmetrizations. Our estimates are polynomial in the dimension and in the logarithm of the desired distance to a Euclidean ball, improving previously known exponential estimates. Inspired by a method of Diaconis [D], our technique involves spherical harmonics. We also make use of an earlier result by the author regarding “isomorphic Minkowski symmetrization”.

Keywords

Early Result Quantitative Estimate Convex Body Spherical Harmonic Exponential Estimate 
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

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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