Krantz, Steven On a theorem of Bers, with applications to the study of automorphism groups of domains. (English) Zbl 1339.32003 Can. Math. Bull. 59, No. 2, 346-353 (2016). 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 Keywords:Bers’ theorem; algebras of holomorphic functions; noncompact automorphism group; biholomorphic equivalence PDFBibTeX XMLCite \textit{S. Krantz}, Can. Math. Bull. 59, No. 2, 346--353 (2016; Zbl 1339.32003) Full Text: DOI arXiv