On the Bergman distance on model domains in $\mathbb C^n$
Volume 116 / 2016
Annales Polonici Mathematici 116 (2016), 1-36
MSC: Primary 32F45; Secondary 32T25, 32U35.
DOI: 10.4064/ap3752-12-2015
Published online: 2 December 2015
Abstract
Let $P$ be a real-valued and weighted homogeneous plurisubharmonic polynomial in $\mathbb C^{n-1}$ and let $D$ denote the ‶model domain″ $\{z \in \mathbb C^n\mid r(z):= \mathop{\rm Re} z_1 + P(z') <0\}$. We prove a lower estimate on the Bergman distance of $D$ if $P$ is assumed to be strongly plurisubharmonic away from the coordinate axes.
