Carathéodory balls in convex complex ellipsoids

Włodzimierz Zwonek

ArticleOriginal scientific text

Title

Carathéodory balls in convex complex ellipsoids

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Affiliations

Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

We consider the structure of Carathéodory balls in convex complex ellipsoids belonging to few domains for which explicit formulas for complex geodesics are known. We prove that in most cases the only Carathéodory balls which are simultaneously ellipsoids "similar" to the considered ellipsoid (even in some wider sense) are the ones with center at 0. Nevertheless, we get a surprising result that there are ellipsoids having Carathéodory balls with center not at 0 which are also ellipsoids.

Keywords

ENG

Carathéodory ball, c-geodesic, convex complex ellipsoid

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Title

Carathéodory balls in convex complex ellipsoids

Affiliations

Abstract

Keywords

Bibliography