no. 3
Meromorphic extension spaces
Annales de l'Institut Fourier, Tome 42 (1992) no. 3, pp. 501-515.

Cet article a pour but d’étudier les espaces de prolongement méromorphe. Les résultats obtenus permettent de conclure à l’invariance du prolongement méromorphe par les applications analytiques surjectives propres finies.

The aim of the present paper is to study meromorphic extension spaces. The obtained results allow us to get the invariance of meromorphic extendibility under finite proper surjective holomorphic maps.

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     author = {Le Mau Hai and Nguyen Van Khue},
     title = {Meromorphic extension spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {501--515},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {42},
     number = {3},
     year = {1992},
     doi = {10.5802/aif.1300},
     mrnumber = {93m:32033},
     zbl = {0768.32018},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1300/}
}
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Le Mau Hai; Nguyen Van Khue. Meromorphic extension spaces. Annales de l'Institut Fourier, Tome 42 (1992) no. 3, pp. 501-515. doi : 10.5802/aif.1300. http://www.numdam.org/articles/10.5802/aif.1300/

[1] K. Adachi, M. Suzuki, M. Yoshida, Continuation of holomorphic mappings with values in complex Lie groups, Pacif. J. Math., 47, (1973), 1-4. | MR | Zbl

[2] G. Dloussky, Enveloppes d'holomorphie et prolongement d'hypersurfaces. Séminaire Pierre Lelong (Analyse), année 1975-1976, Lecture Notes in Math., 578 (1977). | Zbl

[3] F. Docquier, H. Grauert, Levisches problem and Rungescher Satz fur Teilgebiete Steinscher Mannigfaligkeiten, Math. Ann., 140 (1960), 94-123. | MR | Zbl

[4] G. Fischer, Complex Analytic Geometry, Lecture Notes in Math., 538, Springer-Verlag (1976). | MR | Zbl

[5] H. Grauert, R. Remmert, Komplexer Raume, Math. Ann., 136 (1958), 245-318. | MR | Zbl

[6] P.A. Griffiths, Two theorems on extension of holomorphic mappings, Inv. Math., 14 (1971), 27-62. | MR | Zbl

[7] R. Gunning, H. Rossi, Analytic Functions of Several Complex Variables. Prentice-Hall, Englewood Cliffs, N.J, 1965. | MR | Zbl

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

[9] J. Kajiwara, E. Sakai, Generalization of Levi-Oka theorem concerning meromorphic functions, Nagoya. Math. J., 29 (1967), 75-84. | MR | Zbl

[10] H. Kazama, On pseudoconvexity of complex Lie groups. Mem. Fac. Sci. Kyushu Univ., 27 (1973), 241-247. | MR | Zbl

[11] H. Kerner, Uberlagerungen und Holomorphiehullen, Math. Ann., 144 (1961), 126-134. | MR | Zbl

[12] K. Kodaira, On compact analytic surfaces I, Annals of Math., 77 (1963). | MR | Zbl

[13] R. Narasimhan, A note on Stein space and their normalizations, Ann. Scuola Norm. Sup. Pisa., 16 (1962), 327-333. | Numdam | MR | Zbl

[14] R. Remmert, Holomorphe und meromorphe Abbildungen komplexer Raume, Math. Ann., 133 (1957), 328-370. | MR | Zbl

[15] B. Shiffman, Extension of holomorphic maps into hermitian manifolds, Math. Ann., 194 (1971), 249-258. | MR | Zbl

[16] B. Shiffman, Holomorphic and Meromorphic Mappings and Curvature, Math. Ann., 222 (1976), 171-194. | MR | Zbl

[17] Y.T. Siu, Extension of meromorphic maps into Kahler manifolds, Annals of Math., 102 (1975), 421-462. | MR | Zbl

[18] K. Stein, Analytische Zerlegungen Komplexer Raume, Math. Ann., 132, (1956), 63-93. | MR | Zbl

[19] Takeuchi, On completeness of holomorphic principal bundles, Nagoya. Math. J., 57 (1974), 121-138. | Zbl

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