Hyperbolic Reinhardt Domains in C2 with Noncompact Automorphism Group
Alexander V. Isaev, Steven G. Krantz
Abstract
We give an explicit description of hyperbolic Reinhardt domains D in C2 such that: (i) D has Ck-smooth boundary for some k greater than or equal to 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 an example that indicates that the situation in Cn for n greater than or equal to 3 is essentially more complicated than that in C2.
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