On the Green function on a certain class of hyperconvex domains

• Autorzy: Gregor Herbort
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 32F45: Invariant metrics and pseudodistances
• 32U35: Pluricomplex Green functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 94
• Numer: 2
• Strony: 149-185

Daty

wydano

2008

Twórcy

autor

Gregor Herbort

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

Identyfikatory

DOI

10.4064/ap94-2-4