An arithmetic proof of John’s ellipsoid theorem

By Peter M. Gruber, Franz E. Schuster. 2005

74 citations recorded by the source corpus.

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’.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1c406b540621236dfd0e4b14033c39dce81a3fa6

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In Applied Mathematics

1. Du Zou
2. Ge Xiong
3. Yiming Zhao
4. Deping Ye
5. Yong Huang
6. Martin Henk
7. Eva Linke

In Geometry and Topology

1. Du Zou
2. Ge Xiong
3. Yiming Zhao
4. Deping Ye

Citations in the corpus

• Orlicz–John ellipsoids (2014, methodology): “As Gruber and Schuster [21] observed, a symmetric matrix T = (tij)n×n is identified with a point in R 1 2n(n+1), with the coordinate (t11, · · · , t1n, t22, · · · , t2n, · · · , tnn).”