Abstract
Let D be a domain in ℂ2 such that the orbit of an internal point under the group Aut(D) of the holomorphic automorphisms of D accumulates to a smooth boundary point p. It is well known that if p is a strictly pseudoconvex point, such a local information forces D to be biholomorphic to the ball. We prove that if p is only weakly pseudoconvex of finite type, the domain D need not to be biholomorphic to a natural standard model. On the other end our results show that, under some convexity assumptions, D may be realized as a bounded domain with real analytic boundary except at most at one point.
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Landucci, M., Patrizio, G. Unbounded domains in ℂ2 with non-compact automorphisms group. Results. Math. 42, 300–307 (2002). https://doi.org/10.1007/BF03322857
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DOI: https://doi.org/10.1007/BF03322857