Domains with Non-Compact Automorphism Group: A Survey
Alexander V. Isaev and Steven G. Krantz
We survey results arising from the study of domains in $\mathbb C^n$ with non-compact automorphism group. Beginning with a well-known characterization of the unit ball, we develop ideas toward a consideration of weakly pseudoconvex (and even non-pseudoconvex) domains with particular emphasis on characterizations of (i) smoothly bounded domains with non-compact automorphism group and (ii) the Levi geometry of boundary orbit accumulation points.Particular attention will be paid to results derived in the past ten years.