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Hyperconvexity of non-smooth pseudoconvex domains

Xu Wang (2014)

Annales Polonici Mathematici

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.

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