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Let $Z$ be a holomorphic vector field on $\mathbb{C}^n$. I would like to know whether (it seems that it is) the domain $D_\phi \subset \mathbb{C} \times \mathbb{C}^n$ of a maximal flow $\phi: D_\phi \rightarrow \mathbb{C}^n$ associated to $Z$ is pseudoconvex i.e. a domain of holomorphy, since I imagine one argues that way. The question is motivated by Forstneric's article Actions of $\mathbb{R}$ and $\mathbb{C}$ on complex manifolds where in the end of the proof of Proposition 2.1 he uses Kontinuitatssatz for $D_\phi$.

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