The pluricomplex Green function on some regular pseudoconvex domains
Volume 110 / 2014
Annales Polonici Mathematici 110 (2014), 209-226
MSC: Primary 32U35; Secondary 32T25, 32T45.
DOI: 10.4064/ap110-3-1
Abstract
Let $D$ be a smooth bounded pseudoconvex domain in $\mathbb C^n$ of finite type. We prove an estimate on the pluricomplex Green function $\mathscr G_D(z,w)$ of $D$ that gives quantitative information on how fast the Green function vanishes if the pole $w$ approaches the boundary. Also the Hölder continuity of the Green function is discussed.
