On the Green function on a certain class of hyperconvex domains

Gregor Herbort. "On the Green function on a certain class of hyperconvex domains." Annales Polonici Mathematici 94.2 (2008): 149-185. <http://eudml.org/doc/280535>.

@article{GregorHerbort2008,
abstract = {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 $|ψ| ≤ Cexp(-C^\{\prime \}(log(1/δ_D))^α)$ 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.},
author = {Gregor Herbort},
journal = {Annales Polonici Mathematici},
keywords = {pluricomplex Green function; hyperconvex domain; Bergman distance},
language = {eng},
number = {2},
pages = {149-185},
title = {On the Green function on a certain class of hyperconvex domains},
url = {http://eudml.org/doc/280535},
volume = {94},
year = {2008},
}

TY - JOUR
AU - Gregor Herbort
TI - On the Green function on a certain class of hyperconvex domains
JO - Annales Polonici Mathematici
PY - 2008
VL - 94
IS - 2
SP - 149
EP - 185
AB - 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 $|ψ| ≤ Cexp(-C^{\prime }(log(1/δ_D))^α)$ 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.
LA - eng
KW - pluricomplex Green function; hyperconvex domain; Bergman distance
UR - http://eudml.org/doc/280535
ER -