On the Green function on a certain class of hyperconvex domains

Gregor Herbort¹

¹Fachbereich C – Mathematik und Naturwissenschaften Bergische Universität Wuppertal Gaußstraße 20 D-42097 Wuppertal, Germany

Annales Polonici Mathematici, Tome 94 (2008) no. 2, pp. 149-185

Résumé

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 $0\alpha1$. Furthermore, we obtain a Hopf lemma for such a function $\psi$. Finally, we prove a lower bound on the Bergman distance on $D$.

Détail

DOI : 10.4064/ap94-2-4

Keywords: study behavior pluricomplex green function bounded hyperconvex domain admits smooth plurisubharmonic exhaustion function psi psi integrable near boundary moreover satisfies estimate psi leq exp log delta alpha points close enough boundary constants alpha furthermore obtain hopf lemma function psi finally prove lower bound bergman distance