arxiv: 1207.7246 · v1 · pith:ZWUFE4RJnew · submitted 2012-07-31 · 🧮 math.MG · math.DG· math.FA

An arithmetic proof of John's ellipsoid theorem

Peter M. Gruber , Franz E. Schuster This is my paper

classification 🧮 math.MG math.DGmath.FA

keywords johnellipsoidideapartprooftheoremappliesarithmetic

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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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An arithmetic proof of John's ellipsoid theorem

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