Davis' Convexity Theorem and Extremal Ellipsoids

Details Davis' Convexity Theorem and Extremal Ellipsoids Davis' Convexity Theorem and Extremal Ellipsoids

2009-07-07

arxiv.org/abs/0907.1158v2

Beitr. Algebra Geom 51:1 (2010) 263-274

Mathematics

Metric Geometry

10 pages, 4 figures

Scientific paper

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.

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