Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 263-274 (2010)

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Davis' convexity theorem and extremal ellipsoids

Matthias J. Weber and Hans-Peter Schröcker

Unit Geometry and CAD, University Innsbruck, Technikerstraße 13, A6020 Innsbruck, Austria, e-mail:

Abstract: We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on the function used to measure the size of the ellipsoid. Simple examples with non-unique minimal or maximal ellipsoids conclude this article.

Keywords: minimal ellipsoid, maximal ellipsoid, Davis' convexity theorem

Classification (MSC2000): 52A27, 52A20

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Electronic version published on: 27 Jan 2010. This page was last modified: 28 Jan 2013.

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