Abstract

We give an explicit description of hyperbolic Reinhardt domains D ⊂ C² such that: (i) D has C^k-smooth boundary for some k ≥ 1, (ii) D intersects at least one of the coordinate complex lines {z₁ = 0}, {z₂ = 0}, and (iii) D has noncompact automorphism group. We also give an example that explains why such a setting is natural for the case of hyperbolic domains and examples that indicate that the situation in Cⁿ for n ≥ 3 is essentially more complicated than that in C².

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