On the Green function on a certain class of hyperconvex domains

Volume 94 / 2008

Gregor Herbort Annales Polonici Mathematici 94 (2008), 149-185 MSC: 32U35, 32F45. DOI: 10.4064/ap94-2-4


We study the behavior of the pluricomplex Green function on a bounded hyperconvex domain $D$ that admits a smooth plurisubharmonic exhaustion function $\psi$ such that $1/|\psi|$ is integrable near the boundary of $D$, and moreover satisfies the estimate $|\psi | \leq C \exp ( - C' (\log (1/\delta_D)) ^\alpha )$ at points close enough to the boundary with constants $C,C'>0$ and $0<\alpha<1$. Furthermore, we obtain a Hopf lemma for such a function $\psi$. Finally, we prove a lower bound on the Bergman distance on $D$.


  • Gregor HerbortFachbereich C – Mathematik und Naturwissenschaften
    Bergische Universität Wuppertal
    Gaußstraße 20
    D-42097 Wuppertal, Germany

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