Hyperconvexity of non-smooth pseudoconvex domains

Xu Wang. "Hyperconvexity of non-smooth pseudoconvex domains." Annales Polonici Mathematici 111.1 (2014): 1-11. <http://eudml.org/doc/280764>.

@article{XuWang2014,
abstract = {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.},
author = {Xu Wang},
journal = {Annales Polonici Mathematici},
keywords = {hyperconvexity; Lipschitz boundary; holomorphic motion},
language = {eng},
number = {1},
pages = {1-11},
title = {Hyperconvexity of non-smooth pseudoconvex domains},
url = {http://eudml.org/doc/280764},
volume = {111},
year = {2014},
}

TY - JOUR
AU - Xu Wang
TI - Hyperconvexity of non-smooth pseudoconvex domains
JO - Annales Polonici Mathematici
PY - 2014
VL - 111
IS - 1
SP - 1
EP - 11
AB - 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.
LA - eng
KW - hyperconvexity; Lipschitz boundary; holomorphic motion
UR - http://eudml.org/doc/280764
ER -