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On a theorem of Bers, with applications to the study of automorphism groups of domains. (English) Zbl 1339.32003

Summary: We study and generalize a classical theorem of L. Bers that classifies domains up to biholomorphic equivalence in terms of the algebras of holomorphic functions on those domains. Then we develop applications of these results to the study of domains with noncompact automorphism group.

MSC:

32A38 Algebras of holomorphic functions of several complex variables
30H50 Algebras of analytic functions of one complex variable
32A10 Holomorphic functions of several complex variables
32M99 Complex spaces with a group of automorphisms
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