Comparison of the Bergman kernel and the Carath\'eodory--Eisenman volume

Authors :: Nikolov, Nikolai
Thomas, Pascal J.
Source :: Proc. Amer. Math. Soc. 147 (2019), 4915-4919
Publication Year :: 2018
Abstract: 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.<br />Comment: 5 pages