Boundary behavior of the pluricomplex green function

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Let Ω be a bounded domain in Cn. This paper deals with the study of the behavior of the pluricomplex Green function gΩ(z, w) when the pole w tends to a boundary point w0 of Ω. We find conditions on Ω which ensure that limw→w0 gΩ(z, w)=0, uniformly with respect to z on compact subsets of Ω̄\{w0}. Our main result is Theorem 5; it gives a sufficient condition for the above property to hold, formulated in terms of the existence of a plurisubharmonic peak function for Ω at w0 which satisfies a certain growth condition.

Original languageEnglish (US)
Pages (from-to)341-353
Number of pages13
JournalArkiv for Matematik
Volume36
Issue number2
DOIs
StatePublished - Oct 1998
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Boundary behavior of the pluricomplex green function'. Together they form a unique fingerprint.

  • Cite this