HYPERBOLIC REINHARDT DOMAINS IN ℂ^{2} WITH NONCOMPACT AUTOMORPHISM GROUP

ALEXANDER V. ISAEV STEVEN G. KRANTZ

Abstract. We give an explicit description of hyperbolic Reinhardt domains D ⊂ ℂ^{2} such that: (i) D has C^{k}-smooth boundary for some k ≥ 1, (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 an example that indicates that the situation in ℂ^{n} for n ≥ 3 is essentially more complicated than that in ℂ^{2}.