The pluri-complex Green function and a covering mapping. (English) Zbl 0920.32014
Noguchi, J. (ed.) et al., Geometric complex analysis. Proceedings of the conference held at the 3rd International Research Institute of the Mathematical Society of Japan, Hayama, March 19–29, 1995. Singapore: World Scientific. 43-50 (1996).
Let \(G\) and \(D\) be domains in \(\mathbb{C}^n\) and \(\varphi:G\to D\) a covering mapping. The pluricomplex Green functions \(g^G\) and \(g^D\) are compared. Namely, if \(p,q\in D\), \(\{a_0,a_2,\dots\}=\varphi^{-1}(p)\), \(\{b_0,b_1, \dots\}= \varphi^{-1}(q)\), then \(g^D(q,p) \geq\sum_{j\geq 0} g^G(B_j,a_0)\) and \(g^D(q,p) \leq\sum_{j\geq 0} g^G(b_0,a_j)\).
Relations between Azukawa’s pseudometrics on \(G\) and \(D\) are obtained, too.
For the entire collection see [Zbl 0903.00037].
Relations between Azukawa’s pseudometrics on \(G\) and \(D\) are obtained, too.
For the entire collection see [Zbl 0903.00037].
Reviewer: A.Yu.Rashkovsky (Khar’kov)
MSC:
| 32U05 | Plurisubharmonic functions and generalizations |
| 32F45 | Invariant metrics and pseudodistances in several complex variables |
| 31C10 | Pluriharmonic and plurisubharmonic functions |
