Arkiv för Matematik

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  • Volume 36, Number 2 (1998), 341-353.

Boundary behavior of the pluricomplex Green function

Dan Coman

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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→wogΩ(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 w0 which satisfies a certain growth condition.

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Ark. Mat., Volume 36, Number 2 (1998), 341-353.

Received: 30 April 1997
First available in Project Euclid: 31 January 2017

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1998 © Institut Mittag-Leffler


Coman, Dan. Boundary behavior of the pluricomplex Green function. Ark. Mat. 36 (1998), no. 2, 341--353. doi:10.1007/BF02384773.

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