Finitely smooth Reinhardt domains with non-compact automorphism group
  We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and having only finite boundary smoothness is considerably more complicated than the classification of such domains that have infinitely smooth boundary. 
A. V. Isaev and S. G. Krantz