On John-Type Ellipsoids

Details On John-Type Ellipsoids On John-Type Ellipsoids

2003-12-02

arxiv.org/abs/math/0312065v1

Mathematics

Metric Geometry

Scientific paper

Given an arbitrary convex symmetric n-dimensional body, we construct a natural and non-trivial continuous map which associates ellipsoids to ellipsoids, such that the Lowner-John ellipsoid of the body is its unique fixed point. A new characterization of the Lowner-John ellipsoid is obtained, and we also gain information regarding the contact points of inscribed ellipsoids with the body.

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