Hyperbolic Reinhardt domains in ℂ² with noncompact automorphism group

A.V. Isaev and S.G. Krantz

Vol. 184 (1998), No. 1, 149–160

DOI: 10.2140/pjm.1998.184.149

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.

Milestones

Received: 5 November 1996

Published: 1 May 1998