Hyperbolic Reinhardt Domains in C² with Noncompact Automorphism Group

1996/10/31 by Alexander Isaev, Isaev, Alexander V., Steven G. Krantz +1
Mathematics · #32 #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/9610204

openalex publication_date 1996/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit description of hyperbolic Reinhardt domains D in C² such that: (i) D has C^k-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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