An arithmetic proof of John's ellipsoid theorem
Metric Geometry
2012-08-01 v1 Differential Geometry
Functional Analysis
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'.
Cite
@article{arxiv.1207.7246,
title = {An arithmetic proof of John's ellipsoid theorem},
author = {Peter M. Gruber and Franz E. Schuster},
journal= {arXiv preprint arXiv:1207.7246},
year = {2012}
}