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An arithmetic proof of John's ellipsoid theorem (1207.7246v1)
Published 31 Jul 2012 in math.MG, math.DG, and math.FA
Abstract: Using an idea of Voronoi in the geometric theory of positive definite quadratic forms, we give a transparent proof of John's characterization of the unique ellipsoid of maximum volume contained in a convex body. The same idea applies to the 'hard part' of a generalization of John's theorem and shows the difficulties of the corresponding 'easy part'.
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