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Uniqueness results for minimal enclosing ellipsoids. (English) Zbl 1172.52300

Summary: We prove uniqueness of the minimal enclosing ellipsoid with respect to strictly eigenvalue convex size functions. Special examples include the classic case of minimal volume ellipsoids (Löwner ellipsoids), minimal surface area ellipsoids or, more generally, ellipsoids that are minimal with respect to quermass integrals.

MSC:

52A40 Inequalities and extremum problems involving convexity in convex geometry
52A38 Length, area, volume and convex sets (aspects of convex geometry)
52A27 Approximation by convex sets
52A39 Mixed volumes and related topics in convex geometry
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