A characterization of certain weakly pseudoconvex domains
In the context of the problem of giving conditions in order to ensure the possibility to determine the global structure of a bounded domain in \({\mathbb C}^n \) from the local shape of its boundary near a point, the author characterizes certain weakly pseudoconvex domains from the viewpoint of biholomorphic automorphism group. He also gives some assumptions under which such a domain is the underlying set of a generalized complex ellipsoid in \({\mathbb C}^n \). The proofs are mainly based on some extension theorems on proper holomorphic mappings and CR-mappings and on the existence of Webster's CR-invariant metrics on strictly pseudoconvex real analytic hypersurfaces in \({\mathbb C}^n \) without umbilical points.
scientific article; zbMATH DE number 1321873
scientific article