Extremal inscribed and circumscribed complex ellipsoids

Published 29 Dec 2020 in math.MG | (2012.14934v1)

Abstract: 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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