arXiv subjects
Publications and source records attributed to Jorge Luis Arocha.
We prove that two closed subsets of complex space $\C^n$ with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theorem for cosets of closed subgroups of $§^1$.
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.