On the product property of the pluricomplex Green function

Abstract:

We prove that the pluricomplex Green function has the product property $g_{D_{1}\times D_{2}}=\max \{ g_{D_{1}},g_{D_{2}}\}$ for any domains $D_{1}\subset \mathbb {C}^{n}$ and $D_{2}\subset \mathbb {C}^{m}$.