Boundary behavior of the pluricomplex Green function

Dan Coman Department of Mathematics, “Babes-Bolyai” University

TBD mathscidoc:1701.332900

Arkiv for Matematik, 36, (2), 341-353, 1997.4
Let Ω be a bounded domain in$C$^{$n$}. This paper deals with the study of the behavior of the pluricomplex Green function$g$_{Ω}($z, w$) when the pole$w$tends to a boundary point$w$_{0}of Ω. We find conditions on Ω which ensure that lim_{$w→wo$}$g$_{$Ω$}$(z, w)$=0, uniformly with respect to$z$on compact subsets of $$\bar \Omega \backslash \{ w_0 \} $$ . 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$w$_{0}which satisfies a certain growth condition.
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@inproceedings{dan1997boundary,
  title={Boundary behavior of the pluricomplex Green function},
  author={Dan Coman},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203554106890709},
  booktitle={Arkiv for Matematik},
  volume={36},
  number={2},
  pages={341-353},
  year={1997},
}
Dan Coman. Boundary behavior of the pluricomplex Green function. 1997. Vol. 36. In Arkiv for Matematik. pp.341-353. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203554106890709.
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