Carathéodory balls in convex complex ellipsoids

Volume 64 / 1996

Włodzimierz Zwonek Annales Polonici Mathematici 64 (1996), 183-194 DOI: 10.4064/ap-64-2-183-194


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.


  • Włodzimierz Zwonek

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