[Banach] Abstract of a paper by Peter M. Gruber and Franz E. Schuster

This is an announcement for the paper "An arithmetic proof of John’s ellipsoid theorem" by Peter M. Gruber and Franz E. Schuster.

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’.

Archive classification: math.MG math.DG math.FA

Mathematics Subject Classification: 52A21, 46B07, 52A27

Citation: Arch. Math. (Basel) 85 (2005), 82–88

Submitted from: franz.schuster@tuwien.ac.at

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.7246

or

http://arXiv.org/abs/1207.7246