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Abstract

We show that a bounded pseudoconvex domain $D\subset {\mathbb C}^n$ is hyperconvex if its boundary $\partial D$ 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 $\varOmega \subset {\mathbb C}$ is hyperconvex provided every component of $\partial \varOmega $ contains at least two points. Furthermore, we show that hyperconvexity is a Hölder-homeomorphic invariant for planar domains.