Abstract
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.
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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)
Klartag, B.: Rate of convergence of geometric symmetrization. Geom. Funct. Anal. (GAFA) 14(6), 1322–1338 (2004)
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A. Segal was supported by a grant from the European Research Council.
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Florentin, D.I., Segal, A. Minkowski symmetrizations of star shaped sets. Geom Dedicata 184, 115–119 (2016). https://doi.org/10.1007/s10711-016-0159-z
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DOI: https://doi.org/10.1007/s10711-016-0159-z