Abstract
We describe the branch locus of a proper holomorphic mapping between two smoothly bounded pseudoconvex domains of finite type in $\mathbb{C}^2$ under the assumption that the first domain admits a transversal holomorphic action of the unit circle. As an application we show that any proper holomorphic self-mapping of a smoothly bounded pseudoconvex complete circular domain of finite type in $\mathbb{C}^2$ is biholomorphic.
Citation
Bernard Coupet. Yifei Pan. Alexandre Sukhov. "On proper holomorphic mappings from domains with $\bf T$-action." Nagoya Math. J. 154 57 - 72, 1999.
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