Domains with non-compact automorphism group: A survey

We survey results arising from the study of domains in C-n with non-compact automorphism group. Beginning with a well-known characterization of the un it ball, we develop ideas toward a consideration of weakly pseudoconvex (an d even non-pseudoconvex) domains with particular emphasis on characterizati ons of iii smoothly bounded domains with non-compact automorphism group and (ii) the Levi geometry of boundary orbit accumulation points. Particular a ttention will be paid to results derived in the past ten years. (C) 1999 Ac ademic Press.