Rate of convergence of geometric symmetrizations

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dc.creatorKlartag, B.
dc.date2003-12-02
dc.date.accessioned2026-07-07T05:03:29Z
dc.date.available2026-07-07T05:03:29Z
dc.descriptionIt is a classical fact, that given an arbitrary n-dimensional convex body, 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, our technique involves spherical harmonics. We also make use of an earlier result by the author regarding ``isomorphic Minkowski symmetrization''.
dc.descriptionAccepted for publication in Geom. Funct. Anal
dc.identifierhttps://arxiv.org/abs/math/0312064
dc.identifierhttp://arxiv.org/abs/math/0312064
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69440
dc.subjectMetric Geometry
dc.subjectFunctional Analysis
dc.titleRate of convergence of geometric symmetrizations
dc.typetext

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