Hyperbolic Reinhardt Domains in Bbb C^2$ with Noncompact Automorphism Group
Alexander V. Isaev and Steven G. Krantz
We give an explicit description of hyperbolic Reinhardt domains $D \subset {\Bbb C}^2$ such that: ${\bf (i)}$ $D$ has $C^k$-smooth boundary for some $k \geq 1$, ${\bf (ii)}$ $D$ intersects at least one of the coordinate complex lines $\{z_1=0\}$, $\{z_2=0\}$, and ${\bf (iii)}$ $D$ 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 ${\Bbb C}^n$ for $n\ge 3$ is essentially more complicated than that in ${\Bbb C}^2$.