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Domains with non-compact automorphism group: a survey. (English) Zbl 1040.32019
Summary: 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.

##### MSC:
 32M05 Complex Lie groups, group actions on complex spaces 32T15 Strongly pseudoconvex domains
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##### References:
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