Carathéodory balls in convex complex ellipsoids

• Autorzy: Włodzimierz Zwonek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Carathéodory ball; c-geodesic; convex complex ellipsoid

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 2
• Strony: 183-194

Daty

wydano

1996

otrzymano

1995-11-29

Twórcy

autor

Włodzimierz Zwonek

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

Bibliografia

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• [Sc-Sr] B. Schwarz and U. Srebro, Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^n: ‖z‖_p < 1}$, preprint.
• [Sr] U. Srebro, Carathéodory balls and norm balls in $H = {z ∈ ℂ^n: ‖z‖₁ < 1}$, Israel J. Math. 89 (1995), 61-70.
• [Z] W. Zwonek, Carathéodory balls and norm balls of the domains $H_n = {z ∈ ℂ^n: |z₁| + ... + |z_n| < 1}$, Israel J. Math. 89 (1995), 71-76.