Comparison of the Bergman kernel and the Carath\'eodory--Eisenman volume
Abstract
It is proved that for any domain in Cn 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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