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On the Bergman distance on model domains in $\mathbb C^n$

Volume 116 / 2016

Gregor Herbort Annales Polonici Mathematici 116 (2016), 1-36 MSC: Primary 32F45; Secondary 32T25, 32U35. DOI: 10.4064/ap3752-12-2015 Published online: 2 December 2015


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.


  • Gregor HerbortFachbereich Mathematik und Naturwissenschaften
    Bergische Universität Wuppertal
    D-42097 Wuppertal, Germany

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