We show that a bounded pseudoconvex domain D ⊂ ℂⁿ is hyperconvex if its boundary ∂D can be written locally as a complex continuous family of log-Lipschitz curves. We also prove that the graph of a holomorphic motion of a bounded regular domain Ω ⊂ ℂ is hyperconvex provided every component of ∂Ω contains at least two points. Furthermore, we show that hyperconvexity is a Hölder-homeomorphic invariant for planar domains.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-1-1,
author = {Xu Wang},
title = {Hyperconvexity of non-smooth pseudoconvex domains},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {1-11},
zbl = {1297.32019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-1-1}
}
Xu Wang. Hyperconvexity of non-smooth pseudoconvex domains. Annales Polonici Mathematici, Tome 111 (2014) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-1-1/