English

Hyperbolic Reinhardt Domains in C^2 with Noncompact Automorphism Group

Complex Variables 2009-09-25 v1

Abstract

We give an explicit description of hyperbolic Reinhardt domains D in C^2 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}\{z_1=0\}, {z2=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 greater than or equal to 3 is essentially more complicated than that in C^2.

Keywords

Cite

@article{arxiv.math/9610204,
  title  = {Hyperbolic Reinhardt Domains in C^2 with Noncompact Automorphism Group},
  author = {Alexander V. Isaev and Steven G. Krantz},
  journal= {arXiv preprint arXiv:math/9610204},
  year   = {2009}
}
R2 v1 2026-07-22T17:56:27.248Z