Let P be a real-valued and weighted homogeneous plurisubharmonic polynomial in and let D denote the “model domain” z ∈ ℂⁿ | r(z):= Re z₁ + P(z’) < 0. We prove a lower estimate on the Bergman distance of D if P is assumed to be strongly plurisubharmonic away from the coordinate axes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap3752-12-2015,
author = {Gregor Herbort},
title = {On the Bergman distance on model domains in Cn},
journal = {Annales Polonici Mathematici},
volume = {116},
year = {2016},
pages = {1-36},
zbl = {06545354},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3752-12-2015}
}
Gregor Herbort. On the Bergman distance on model domains in ℂⁿ. Annales Polonici Mathematici, Tome 116 (2016) pp. 1-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3752-12-2015/