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Remarks on the pluricomplex Green function. (English) Zbl 0848.31007
Authors’ summary: We prove that the pluricomplex Green function $$g$$ and the Azukawa pseudometric $$A$$ have the product property on $$G_1 \times G_2$$ if $$G_2$$ is pseudoconvex. Moreover, we show that $$g_G$$ and $$A_G$$ are upper semicontinuous for any domain $$G \subset \mathbb{C}^n$$. Explicit examples are given.

##### MSC:
 31C10 Pluriharmonic and plurisubharmonic functions 32F99 Geometric convexity in several complex variables
##### Keywords:
pluricomplex Green function; Azukawa pseudometric
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