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2 dimensional counterexamples to generalizations of the Levi problem. (English) Zbl 0379.32016


MSC:

32E10 Stein spaces
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References:

[1] Behnke, H., Stein, K.: Konvergente Folgen von Regularitätsbereichen und die Meromorphiekonvexität. Math. Ann.116, 204-216 (1938-1939) · JFM 64.0322.03 · doi:10.1007/BF01597355
[2] Bremermann, H.: Über die Äquivalenz der pseudokonvexen Gebiete und der Holomorphiegebiete im Raum vonn komplexen Veränderlichen. Math. Ann.128, 63-91 (1954) · Zbl 0056.07801 · doi:10.1007/BF01360125
[3] Diederich, K., Fornæss, J.E.: Pseudoconvex Domains: Bounded Strictly Plurisubharmonic Exhaustion Functions. Invent. Math.39, 129-141 (1977) · Zbl 0353.32025 · doi:10.1007/BF01390105
[4] Fornæss, J.E.: An increasing sequences of Stein manifold whose limit is not Stein. Math. Ann.223, 275-277 (1976) · Zbl 0334.32017 · doi:10.1007/BF01360958
[5] Grauert, H.: On Levi’s problem and the embedding of real-analytic manifolds. Ann. of Math.68, 460-472 (1958) · Zbl 0108.07804 · doi:10.2307/1970257
[6] Levi, E.E.: Studii sui puncti singolari essenziale delle funzioni analitiche di due o più variabili complesse. Ann. Mat. pur appl. Serie III. Tomo17, 61-87 (1910) · JFM 41.0487.01
[7] Narasimhan, R.: The Levi Problem in the theory of functions of several complex variables. ICM Stockholm (1962) · Zbl 0131.30801
[8] Norguet, F.: Sur les domaines d’holomorphie des fonctions uniformes de plusieurs variables complexes. Bull. Soc. Math. France.82, 137-159 (1954) · Zbl 0056.07701
[9] Oka, K.: Sur les fonctions analytiques de plusieurs variables. VI. Domaines pseudoconvexes. Tohoku Math. J. II, Ser.49, 19-52 (1942) · Zbl 0060.24006
[10] Oka, K.: Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique interieur. Jap. J. Math.23, 97-155 (1953) · Zbl 0053.24302
[11] Serre, J.P.: Quelques problèmes globaux relatifs aux variétés de Stein. Colloque sur les fonctions de plusieurs variables, pp. 57-68, Bruxelles 1953
[12] Skoda, H.: Fibrés holomorphes à base et à fibre de Stein. To appear · Zbl 0353.32032
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