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Diederich, Klas; Ohsawa, Takeo

A Levi problem on two-dimensional complex manifolds. (English) Zbl 0502.32010

Math. Ann. 261, 255-261 (1982).
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Cited in 16 Documents

MSC:

32E10 Stein spaces
32E05 Holomorphically convex complex spaces, reduction theory
32T99 Pseudoconvex domains

Keywords:

pseudoconvex boundary; real analytic boundary; holomorphically convex; compact domain; Levi flat boundary; modification of Stein space; Steinness

Citations:

Zbl 0417.32010; Zbl 0394.32012
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Full Text: DOI EuDML

References:

[1] Brun, J.: Le problème de Levi dans les fibrés à base de Stein et à fibre une courbe compacte. Ann. Inst. Fourier (Grenoble)27, 17-28 (1977) · Zbl 0352.32025
[2] Diederich, K., Fornaess, J.E.: Pseudoconvex domains: an example with nontrivial Nebenhülle. Math. Ann.225, 275-292 (1977) · doi:10.1007/BF01425243
[3] Diederich, K., Fornaess, J.E.: Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions. Invent. Math.39, 129-141 (1977) · Zbl 0353.32025 · doi:10.1007/BF01390105
[4] Diederich, K., Fornaess, J.E.: Pseudoconvex domains: existence of Stein neighbourhoods. Duke Math. J.44, 641-662 (1977) · Zbl 0381.32014 · doi:10.1215/S0012-7094-77-04427-1
[5] Diederich, K., Fornaess, J.E.: Proper holomorphic maps onto pseudoconvex domains with real analytic boundary. Ann. Math.110, 575-592 (1979) · doi:10.2307/1971240
[6] Grauert, H.: On Levi’s problem and the imbedding of real-analytic manifolds. Ann. Math.68, 263-273 (1958) · Zbl 0081.07401 · doi:10.1007/BF01351803
[7] Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann.146, 331-368 (1962) · Zbl 0173.33004 · doi:10.1007/BF01441136
[8] Grauert, H.: Bemerkenswerte pseudokonvexe Mannigfaltigkeiten. Math. Z.81, 377-391 (1963) · Zbl 0151.09702 · doi:10.1007/BF01111528
[9] Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley 1978 · Zbl 0408.14001
[10] Michel, D.: Sur les outverts pseudoconvexes des espaces homogènes. C. R. Acad. Sci. Paris Ser. A283, 779-782 (1976) · Zbl 0355.32019
[11] Narasimhan, R.: The Levi problem in the theory of functions of several complex variables. Proc. Int. Congr. Math. (Stockholm 1962), pp. 385-388. Uppsala: Almquist and Wiksells 1963
[12] Ueda, T.: On the neighbourhood of a compact complex curve with topologically trivial normal bundle, J. Math. Kyoto Univ. (to appear) · Zbl 0519.32019
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