## Arkiv för Matematik

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

### Boundary behavior of the pluricomplex Green function

Dan Coman

#### 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→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.

#### Article information

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

Dates
First available in Project Euclid: 31 January 2017

https://projecteuclid.org/euclid.afm/1485898606

Digital Object Identifier
doi:10.1007/BF02384773

Mathematical Reviews number (MathSciNet)
MR1650450

Zentralblatt MATH identifier
1021.32015

Rights

#### Citation

Coman, Dan. Boundary behavior of the pluricomplex Green function. Ark. Mat. 36 (1998), no. 2, 341--353. doi:10.1007/BF02384773. https://projecteuclid.org/euclid.afm/1485898606

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