On proper $\mbb{R}$-actions on hyperbolic Stein surfaces

Details On proper $\mbb{R}$-actions on hyperbolic Stein surfaces On proper $\mbb{R}$-actions on hyperbolic Stein surfaces

2009-06-18

arxiv.org/abs/0906.3395v1

Documenta Math. 14 (2009), 673--689.

Mathematics

Complex Variables

15 pages

Scientific paper

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

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