We prove that the Bergman metric on domains satisfying condition S is complete. This implies that any bounded pseudoconvex domain with Lipschitz boundary is complete with respect to the Bergman metric. We also show that bounded hyperconvex domains in the plane and convex domains in are Bergman comlete.
@article{bwmeta1.element.bwnjournal-article-apmv71z3p241bwm,
author = {Bo-Yong Chen},
title = {Completeness of the Bergman metric on non-smooth pseudoconvex domains},
journal = {Annales Polonici Mathematici},
volume = {72},
year = {1999},
pages = {241-251},
zbl = {0937.32014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv71z3p241bwm}
}
Bo-Yong Chen. Completeness of the Bergman metric on non-smooth pseudoconvex domains. Annales Polonici Mathematici, Tome 72 (1999) pp. 241-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv71z3p241bwm/
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