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arxiv 2212.05049 v1 pith:BGGXHCSB submitted 2022-12-09 math.MG

An overview of complex ellipsoids

classification math.MG
keywords complexellipsoidsaffinecharacterizationsellipsoidtransformationattentionball
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An ellipsoid is the image of a ball under an affine transformation. If this affine transformation is over the complex numbers, we refer to it as a complex ellipsoid. Characterizations of real ellipsoids have received much attention over the years however, characterizations of complex ellipsoids have been studied very little. This paper is a review of what is known about complex ellipsoids from the point of view of convex geometry. In particular, the proof of the Complex Banach Conjecture.

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