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Carathéodory balls in convex complex ellipsoids

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Zwonek W.

Annales Polonici Mathematici

1996

tom 64

nr 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.

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1 Annales Polonici Mathematici

1 Zwonek W.

1 1996

Wyniki wyszukiwania

Carathéodory balls in convex complex ellipsoids