DOMAINS WITH NON-COMPACT AUTOMORPHISM GROUP: A SURVEY

ALEXANDER V. ISAEV STEVEN G. KRANTZ

Abstract. We survey results arising from the study of domains in ℂ^{n} with noncompact 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.