Hyperbolic Reinhardt domains in C-2 with noncompact automorphism group

摘要

We give an explicit description of hyperbolic Reinhardt domains D subset of C-2 such that: (i) D has C-k-smooth boundary for some k greater than or equal to i, (ii) D intersects at least one of the coordinate complex lines {z(1) = 0}, {z(2) = 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 C-n for n greater than or equal to 3 is essentially more complicated than that in C-2. [References: 14]