On proper $\mathbb{R}$-actions on hyperbolic Stein surfaces
Résumé
In this paper we investigate proper $\mathbb{R}$--actions on hyperbolic Stein surfaces and prove in particular the following result: Let $D\subset\mathbb{C}^2$ be a simply-connected bounded domain of holomorphy which admits a proper $\mathbb{R}$--action by holomorphic transformations. The quotient $D/\mathbb{Z}$ with respect to the induced proper $\mathbb{Z}$--action is a Stein manifold. A normal form for the domain $D$ is deduced.
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