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تسجيل مستخدم جديدComparison of the Bergman kernel and the Caratheodory--Eisenman volume
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It is proved that for any domain in $mathbb C^n$ the Caratheodory--Eisenman volume is comparable with the volume of the indicatrix of the Caratheodory metric up to small/large constants depending only on $n.$ Then the multidimensional Suita conjecture theorem of Blocki and Zwonek implies a comparable relationship between these volumes and the Bergman kernel.
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