Journal of the
Korean Mathematical Society JKMS

We survey results, obtained in the past three years, on characterizing bounded (and Kobayashi-hyperbolic) Reinhardt domains by their automorphism groups. Specifically, we consider the following two situations: (i) the group is non-compact, and (ii) the dimension of the group is sufficiently large. In addition, we prove two theorems on characterizing general hyperbolic complex manifolds by the dimensions of their automorphism groups.

Keywords: Reinhardt domains, hyperbolic complex manifolds, automorphism groups, equivalence problem

MSC numbers: 32A07, 32H02, 32H20, 32M05