Pseudoconvex domains over $q$-complete manifolds

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1. [1] L. Alessandrini - A. Silva, On a theorem of Lelong, Math. Nachr.147 (1990), 83-88. Zbl0722.32009MR1127312
2. [2] A. Andreotti - H. Grauert, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France90 (1962), 193-259. Zbl0106.05501MR150342
3. [3] E. Ballico, Coverings of complex spaces and q-completeness, Riv. Mat. Univ. Parma (4) 7 (1981), 443-452. Zbl0488.32006MR671391
4. [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. Zbl0335.55006MR374476
5. [5] M. Coltoiu, Complete locally pluripolar sets, J. reine angew. Math.412 (1990), 108-112. Zbl0711.32008MR1074376
6. [6] J.-P. Demailly, Cohomology of q-convex spaces in top degrees, Math. Z.204 (1990), 283-295. Zbl0682.32017MR1055992
7. [7] K. Diederich - J.-E. Forness, Smoothing q-convex functions and vanishing theorems, Invent. Math. 82 (1985), 291-305. Zbl0586.32022MR809717
8. [8] F. Docquier - H. Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann.140 (1960), 94-123. Zbl0095.28004MR148939
9. [9] J.-E. Fornæss, A counterexample for the Levi problem for branched Riemann domains over Cn, Math. Ann.234 (1978), 275-277. Zbl0427.32014MR492397
10. [10] J.-E. Fornæss - N. Sibony, Oka's inequality for currents and applications, Math. Ann.301 (1995), 399-419. Zbl0832.32010MR1324517
11. [11] O. Fujita, Domaines pseudoconvexes d'ordre général et fonctions pseudoconvexes d'ordre général, J. Math. Kyoto Univ.30 (1990), 637-649. Zbl0728.32009MR1088347
12. [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. [13] R. Fujita, Domaines sans point critique intérieur sur l'espace projectif complexe, J. Math. Soc. Japan15 (1963), 443-474. Zbl0138.06404MR159034
14. [14] H. Grauert, On Levi's problem and the imbedding of real analytic manifolds, Ann. of Math.68 (1958), 460-472. Zbl0108.07804MR98847
15. [15] H. Grauert, Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Z.81 (1963), 377-391. Zbl0151.09702MR168798
16. [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. Zbl0073.30301MR88028
17. [17] H. Grauert - R. Remmert, Singularitäten komplexer Mannigfaltigkeiten und Riemannsche Gebiete, Math. Z.67 (1957), 103-128. Zbl0077.28902MR87186
18. [18] E.E. Greene - H. Wu, C∞ approximation of convex, subharmonic, and plurisubharmonic functions, Ann. Sci. École Norm. Sup.12 (1979), 47-84. Zbl0415.31001
19. [19] A. Hirschowitz, Pseudoconvexité au-dessus d'espaces plus au moins homogènes, Invent. Math.26 (1974), 303-322. Zbl0275.32009MR357857
20. [20] A. Hirschowitz, Le problème de Levi pour les espaces homogènes, Bull. Soc. Math. France103 (1975), 191-201. Zbl0316.32004MR399510
21. [21] L.R. Hunt - J.J. Murray, q-plurisubharmonic functions and a generalized Dirichlet problem, Michigan Math. J.25 (1978), 299-316. Zbl0378.32013MR512901
22. [22] B. Jennane, Problème de Levi et morphisme localement de Stein, Math. Ann.256 (1981), 37-42. Zbl0491.32012MR620120
23. [23] P. Le Barz, A propos des revêtments ramifiés d'espaces de Stein, Math. Ann.222 (1976), 63-69. Zbl0328.32012MR417449
24. [24] P. Lelong, Domaines convexex par rapport aux fonctions plurisousharmoniques, J. Analyse Math.2 (1952), 178-208. Zbl0049.18102MR54736
25. [25] K. Matsumoto, Pseudoconvex domains of general order over Stein manifolds, Kyushu J. Math.44 (1990), 95-107. Zbl0719.32010MR1072304
26. [26] K. Matsumoto, Boundary distance functions and q-convexity of pseudoconvex domains of general order in Kähler manifolds, J. Math. Soc. Japan48 (1996), 85-107. Zbl0860.32003MR1361549
27. [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. Zbl0116.06103MR176096
28. [28] F. Norquet - Y.-T. Siu, Holomorphic convexity of analytic cycle, Bull. Soc. math. France105 (1977), 191-223. Zbl0382.32010MR590090
29. [29] K. Oka, Domaines finis sans point critique intérieur, Japan. J. Math.27 (1953), 97-155. Zbl0053.24302MR71089
30. [30] M. Peternell, Continuous q-convex exhaustion functions, Invent. Math.85 (1986), 249-262. Zbl0599.32016MR846928
31. [31] M. Peternell, q-completeness of subsets in complex projective space, Math. Z.195 (1987), 443-450. Zbl0611.32008MR895316
32. [32] M. Peternell, Algebraische Varietäten und q-vollständige komplexe Räume, Math. Z.200 (1989), 547-581. Zbl0675.32014MR987586
33. [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. Zbl0309.32011MR399524
34. [34] Y.-T. Siu - S.-T. Yau, Compact Kähler manifolds of positive bisectional curvature, Invent. Math.59 (1980), 189-204. Zbl0442.53056MR577360
35. [35] A. Takeuchi, Domaines pseudoconvexes infinis et la métrique riemanniene dans un espace projectif, J. Math. Soc. Japan16 (1964), 159-181. Zbl0141.08804MR173789
36. [36] A. Takeuchi, Domaines pseudoconvexes sur les variétés kählériennes, J. Math. Kyoto Univ.6 (1967), 323-357. Zbl0179.12203MR217335
37. [37] T. Ueda, Pseudoconvex domains over Grassmann manifolds, J. Math. Kyoto Univ.20 (1980), 391-394. Zbl0456.32011MR582173
38. [38] V. Vâjâitu, On the equivalence of the definitions of q-convex spaces, Arch. Math.61 (1993), 567-575. Zbl0816.32014MR1254069
39. [39] V. Vâjâitu, Approximation theorems and homology of q-Runge domains in complex spaces, J. Reine Angew. Math.449 (1994), 179-199. Zbl0795.32004MR1268585
40. [40] V. Vâjâitu, Local q-complete open sets in Stein spaces with isolated singularities, Kyushu J. Math.51 (1997), 355-368. Zbl0917.32012MR1470159
41. [41] V. Vâjâitu, One dimensional fibering over q-complete spaces, Nagoya Math. J. 151 (1998), 99-106. Zbl0927.32010MR1650281
42. [42] V. Vâjâitu, A Levi problem for continuous strongly q-plurisubharmonic functions, C. R. Acad. Sci. Paris328 (1999), 573-578. Zbl0935.31006MR1679998