Abstract
We show how existing results of stability for Brunn-Minkowski and related inequalities imply results regarding rate of convergences of Minkowski and Blaschke symmetrization processes to the Euclidean ball. To be more precise, the results imply that the amount of symmetrizations needed to approach the Euclidean ball within some distance ε, a polynomial number of symmetrizations (in the dimension and \(\frac{1} {\epsilon }\)) suffice.
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Segal, A. (2014). On Convergence of Blaschke and Minkowski Symmetrization Through Stability Results. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_29
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DOI: https://doi.org/10.1007/978-3-319-09477-9_29
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