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Weakly 1-complete manifold and Levi problem. (English) Zbl 0465.32011

MSC:
32E05 Holomorphically convex complex spaces, reduction theory
32F10 \(q\)-convexity, \(q\)-concavity
32L20 Vanishing theorems
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[1] Grauert, H., Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Z., 81 (1963), 377-391. · Zbl 0151.09702 · doi:10.1007/BF01111528 · eudml:170159
[2] Gunning, R. C. and Rossi, H., Analytic functions of several complex variables, Engelwood Cliffs, N. J. Prentice-Hall, 1965. · Zbl 0141.08601
[3] Hirschowitz, A., Le probleme de Levi pour les espaces homogenes, Bull. Soc. Math. France, 103 (1975), 191-201. · Zbl 0316.32004 · numdam:BSMF_1975__103__191_0 · eudml:87250
[4] Knorr, K. and Schneider, M., Relativexzeptionelle analytische Mengen, Math. Ann., 193 (1971), 238-254. · Zbl 0222.32008 · doi:10.1007/BF02052395 · eudml:182724
[5] Kodaira, K., A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds, Ann. of Math., 75 (1962), 146-162. f6j Narashimhan, R., The Levi problem for complex spaces 11, Math. Ann., 146 (1962), 195-216. · Zbl 0112.38404 · doi:10.2307/1970424
[6] Nakano, S., Vanishing theorems for weakly 1-compleie manifolds 11, Publ. RIMS, Kyoto Univ., 10 (1974), 101-110. · Zbl 0298.32019 · doi:10.2977/prims/1195192175
[7] Richberg, R., Stetige streng pseudokonvexe Funktionen, Math. Ann., 175 (1968), 257-286. · Zbl 0153.15401 · doi:10.1007/BF02063212 · eudml:161667
[8] Siu, Y. T., Pbeudoconvexity and the problem of Levi, Bull. Amer. Math. Soc., 84 (1978), 481-512. · Zbl 0423.32008 · doi:10.1090/S0002-9904-1978-14483-8
[9] Spivak, M., Differential geometry, 4, Publish or Perish Inc., 1975. · Zbl 0306.53002
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