Pseudoconvex domains over q-complete manifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 3, pp. 503-530.
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     title = {Pseudoconvex domains over $q$-complete manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {503--530},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
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     zbl = {1015.32013},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_2000_4_29_3_503_0/}
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Vâjâitu, Viorel. Pseudoconvex domains over $q$-complete manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 3, pp. 503-530. http://archive.numdam.org/item/ASNSP_2000_4_29_3_503_0/

[1] L. Alessandrini - A. Silva, On a theorem of Lelong, Math. Nachr. 147 (1990), 83-88. | MR | Zbl

[2] A. Andreotti - H. Grauert, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193-259. | Numdam | MR | Zbl

[3] E. Ballico, Coverings of complex spaces and q-completeness, Riv. Mat. Univ. Parma (4) 7 (1981), 443-452. | MR | Zbl

[4] A. Cassa, Formule di Künneth per la coomologia a valori in un fascio, Ann. Sc. Norm. Sup. Pisa Cl. Sci. 27 (1973), 905-931. | Numdam | MR | Zbl

[5] M. Coltoiu, Complete locally pluripolar sets, J. reine angew. Math. 412 (1990), 108-112. | MR | Zbl

[6] J.-P. Demailly, Cohomology of q-convex spaces in top degrees, Math. Z. 204 (1990), 283-295. | MR | Zbl

[7] K. Diederich - J.-E. Forness, Smoothing q-convex functions and vanishing theorems, Invent. Math. 82 (1985), 291-305. | MR | Zbl

[8] F. Docquier - H. Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960), 94-123. | MR | Zbl

[9] J.-E. Fornæss, A counterexample for the Levi problem for branched Riemann domains over Cn, Math. Ann. 234 (1978), 275-277. | MR | Zbl

[10] J.-E. Fornæss - N. Sibony, Oka's inequality for currents and applications, Math. Ann. 301 (1995), 399-419. | MR | Zbl

[11] O. Fujita, Domaines pseudoconvexes d'ordre général et fonctions pseudoconvexes d'ordre général, J. Math. Kyoto Univ. 30 (1990), 637-649. | MR | Zbl

[12] O. Fujita, On the equivalence of the q-plurisubharmonic functions and the pseudoconvex functions of general order, Ann. Reports of Graduate School of Human Culture, Nara Women's Univ. 7 (1992), 77-81.

[13] R. Fujita, Domaines sans point critique intérieur sur l'espace projectif complexe, J. Math. Soc. Japan 15 (1963), 443-474. | MR | Zbl

[14] H. Grauert, On Levi's problem and the imbedding of real analytic manifolds, Ann. of Math. 68 (1958), 460-472. | MR | Zbl

[15] H. Grauert, Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Z. 81 (1963), 377-391. | MR | Zbl

[16] H. Grauert - R. Remmert, Konvexität in der komplexen Analysis. Nicht-holomorphkonvexe Holomorphiegebiete und Anwendungen auf die Abbildungstheorie, Comment. Math. Helv. 31 (1956/57), 152-183. | MR | Zbl

[17] H. Grauert - R. Remmert, Singularitäten komplexer Mannigfaltigkeiten und Riemannsche Gebiete, Math. Z. 67 (1957), 103-128. | MR | Zbl

[18] E.E. Greene - H. Wu, C∞ approximation of convex, subharmonic, and plurisubharmonic functions, Ann. Sci. École Norm. Sup. 12 (1979), 47-84. | Numdam | Zbl

[19] A. Hirschowitz, Pseudoconvexité au-dessus d'espaces plus au moins homogènes, Invent. Math. 26 (1974), 303-322. | MR | Zbl

[20] A. Hirschowitz, Le problème de Levi pour les espaces homogènes, Bull. Soc. Math. France 103 (1975), 191-201. | Numdam | MR | Zbl

[21] L.R. Hunt - J.J. Murray, q-plurisubharmonic functions and a generalized Dirichlet problem, Michigan Math. J. 25 (1978), 299-316. | MR | Zbl

[22] B. Jennane, Problème de Levi et morphisme localement de Stein, Math. Ann. 256 (1981), 37-42. | MR | Zbl

[23] P. Le Barz, A propos des revêtments ramifiés d'espaces de Stein, Math. Ann. 222 (1976), 63-69. | MR | Zbl

[24] P. Lelong, Domaines convexex par rapport aux fonctions plurisousharmoniques, J. Analyse Math. 2 (1952), 178-208. | MR | Zbl

[25] K. Matsumoto, Pseudoconvex domains of general order over Stein manifolds, Kyushu J. Math. 44 (1990), 95-107. | MR | Zbl

[26] K. Matsumoto, Boundary distance functions and q-convexity of pseudoconvex domains of general order in Kähler manifolds, J. Math. Soc. Japan 48 (1996), 85-107. | MR | Zbl

[27] R. Narasimhan, "The Levi problem in the theory of several complex variables", Proc. Intemat. Congr. Mathematicians (Sockholm, 1962), 383-385, Inst. Mittag-Leffler, Djursholm. | MR | Zbl

[28] F. Norquet - Y.-T. Siu, Holomorphic convexity of analytic cycle, Bull. Soc. math. France 105 (1977), 191-223. | Numdam | MR | Zbl

[29] K. Oka, Domaines finis sans point critique intérieur, Japan. J. Math. 27 (1953), 97-155. | MR | Zbl

[30] M. Peternell, Continuous q-convex exhaustion functions, Invent. Math. 85 (1986), 249-262. | MR | Zbl

[31] M. Peternell, q-completeness of subsets in complex projective space, Math. Z. 195 (1987), 443-450. | MR | Zbl

[32] M. Peternell, Algebraische Varietäten und q-vollständige komplexe Räume, Math. Z. 200 (1989), 547-581. | MR | Zbl

[33] J.-L. Stehlé, Fonctions plurisousharmoniques et convexité holomorphe de certain fibrés analytique, Sém. P. Lelong (Analyse), 1973/74, Lecture Notes in Math., Vol. 474, Springer, Berlin, 1975, pp. 155-179. | MR | Zbl

[34] Y.-T. Siu - S.-T. Yau, Compact Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), 189-204. | MR | Zbl

[35] A. Takeuchi, Domaines pseudoconvexes infinis et la métrique riemanniene dans un espace projectif, J. Math. Soc. Japan 16 (1964), 159-181. | MR | Zbl

[36] A. Takeuchi, Domaines pseudoconvexes sur les variétés kählériennes, J. Math. Kyoto Univ. 6 (1967), 323-357. | MR | Zbl

[37] T. Ueda, Pseudoconvex domains over Grassmann manifolds, J. Math. Kyoto Univ. 20 (1980), 391-394. | MR | Zbl

[38] V. Vâjâitu, On the equivalence of the definitions of q-convex spaces, Arch. Math. 61 (1993), 567-575. | MR | Zbl

[39] V. Vâjâitu, Approximation theorems and homology of q-Runge domains in complex spaces, J. Reine Angew. Math. 449 (1994), 179-199. | MR | Zbl

[40] V. Vâjâitu, Local q-complete open sets in Stein spaces with isolated singularities, Kyushu J. Math. 51 (1997), 355-368. | MR | Zbl

[41] V. Vâjâitu, One dimensional fibering over q-complete spaces, Nagoya Math. J. 151 (1998), 99-106. | MR | Zbl

[42] V. Vâjâitu, A Levi problem for continuous strongly q-plurisubharmonic functions, C. R. Acad. Sci. Paris 328 (1999), 573-578. | MR | Zbl