×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI