Geodesic
Carathéodory balls in convex complex ellipsoids
Annales Polonici Mathematici, Tome 64 (1996) no. 2, pp. 183-194 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap-64-2-183-194
Keywords: Carathéodory ball, c-geodesic, convex complex ellipsoid

Włodzimierz Zwonek 1

1 
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Włodzimierz Zwonek. Carathéodory balls in convex complex ellipsoids. Annales Polonici Mathematici, Tome 64 (1996) no. 2, pp. 183-194. doi: 10.4064/ap-64-2-183-194

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