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Extremal inscribed and circumscribed complex ellipsoids

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arxiv 2012.14934 v1 pith:Z5DQ5LPZ submitted 2020-12-29 math.MG

Extremal inscribed and circumscribed complex ellipsoids

Jorge L. Arocha , Javier Bracho , Luis Montejano This is my paper
classification math.MG
keywords complexcircumscribedinscribedotherprovevolumeanalogeapplication
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We prove that if a convex set in Cn contains two inscribed complex ellipsoid of maximal volume then one is a translate of the other. On the other hand, the circumscribed complex elipsoid of minimal volume is unique. As application we prove the complex analoge of Brunn's characterization of ellipsods.

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