2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69441Given 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.Metric GeometryFunctional Analysistext