Techniques for studying automorphisms of weakly pseudoconvex domains. (English) Zbl 0779.32017

Greene, Robert E.; Krantz, Steven G.

Several complex variables, Proc. Mittag-Leffler Inst., Stockholm/Swed. 1987-88, Math. Notes 38, 389-410 (1993).

[For the entire collection see Zbl 0759.00008.]
The paper presents a survey of several techniques for studying automorphisms of weakly pseudoconvex domains. It contains the following sections: a) a general localization principle for automorphisms b) Bergman metric localization and its applications in the strongly pseudoconvex case c) the applications of Bergman metric localization in the weakly pseudoconvex case d) the \(C/K\) invariant in boundary localization e) finite type f) Kodama’s theorem on domains biholomorphic to \(\{(z_ 1,z_ 2)/| z_ 1|^{2m_ 1}+\cdots+| z_ n|^{2m_ n}<1\}\) g) the “blow up” technique.

Reviewer: N.Mihalache (Bucureşti)

MSC:

32T99	Pseudoconvex domains
32M05	Complex Lie groups, group actions on complex spaces

Keywords:

survey; automorphisms; weakly pseudoconvex domains

Citations:

Zbl 0759.00008