We study the behavior of the pluricomplex Green function on a bounded hyperconvex domain D that admits a smooth plurisubharmonic exhaustion function ψ such that 1/|ψ| is integrable near the boundary of D, and moreover satisfies the estimate at points close enough to the boundary with constants C,C’ > 0 and 0 < α < 1. Furthermore, we obtain a Hopf lemma for such a function ψ. Finally, we prove a lower bound on the Bergman distance on D.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-4,
author = {Gregor Herbort},
title = {On the Green function on a certain class of hyperconvex domains},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {149-185},
zbl = {1166.32021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-4}
}
Gregor Herbort. On the Green function on a certain class of hyperconvex domains. Annales Polonici Mathematici, Tome 93 (2008) pp. 149-185. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-4/