Berteloot, F.; Cœuré, Gérard Domaines de \({\mathbb{C}}^ 2\), pseudoconvexes et de type fini ayant un groupe non compact d’automorphismes. (On domains in \({\mathbb{C}}^ 2\), being pseudoconvex and of finite type, with non-compact automorphism group). (French) Zbl 0711.32016 Ann. Inst. Fourier 41, No. 1, 77-86 (1991). It is shown that a bounded pseudo-convex domain in \({\mathbb{C}}^ 2\), with smooth boundary and finite type, which has a non-compact automorphism group, is biholomorphically equivalent to a domain \(\{Re w+P(z)<0\}\) where P is polynomial, subharmonic, with degree less than the type of the boundary. Reviewer: F.Berteloot and G.Coeuré Cited in 17 Documents MSC: 32M99 Complex spaces with a group of automorphisms 32T99 Pseudoconvex domains 32A17 Special families of functions of several complex variables Keywords:normal family; bounded pseudo-convex domain; smooth boundary; finite type; non-compact automorphism group PDF BibTeX XML Cite \textit{F. Berteloot} and \textit{G. Cœuré}, Ann. Inst. Fourier 41, No. 1, 77--86 (1991; Zbl 0711.32016) Full Text: DOI Numdam References: [1] E. BEDFORD and S. PINČUK, Domains in C2 with non compact holomorphic automorphism groups, Math. USSR Sbornik, Vol. 63, (1989), 141-151. · Zbl 0668.32029 [2] D. CATLIN, Estimates of invariant metrics on pseudoconvex domains of dimension two, Math., Z., 200, (1989), 429-466. · Zbl 0661.32030 [3] J.E. FORNAESS and N. SIBONY, Construction of p.s.h. functions on weakly pseudoconvex domains, Duke Math., J. 58, 633-655. · Zbl 0679.32017 [4] J.E. FORNAESS and B. STENSONES, Lectures on counterexamples in several complex variables, Mathematical Notes, Princeton University Press. · Zbl 0626.32001 [5] R.E. GREENE and S.G. KRANTZ, Characterizations of certain weakly pseudoconvex domains with non compact automorphism groups, Lecture Notes in Math., 1268, (1987), 121-157. · Zbl 0626.32023 [6] S. PINČUK, Holomorphic maps in cn and the problem of holomorphic equivalence, Encyclopaedia of Mathematical Sciences, Vol. 19, Springer Verlag (1989). [7] R. RICHBERG, Stetige streng pseudokonvexe funktionen, Math. Ann., 175 (1968), 251-286. · Zbl 0153.15401 [8] J.P. ROSAY, Sur une caractérisation de la boule parmi LES domaines de cn par son groupe d’automorphismes, Ann. Inst. Fourier, 29-4 (1979), 91-97. · Zbl 0402.32001 [9] N. SIBONY, Une classe de domaines pseudoconvexes, Duke Math. J., 55, n°2 (1987), 299-319. · Zbl 0622.32016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.