Comparison of the Bergman kernel and the Carathéodory--Eisenman volume

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.

5 pages

References in corpus (1)

• Estimates for the Bergman Kernel and the Multidimensional Suita Conjecture

Cited by in corpus (2)

• Boundary behaviour of the Carathéodory and Kobayashi-Eisenman volume elements
• Geometric estimates and comparability of Eisenman volume elements with the Bergman kernel on (C-)convex domains