no. 4
The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman
Annales de l'Institut Fourier, Tome 46 (1996) no. 4, pp. 1083-1094.

On donne une démonstration simple du théorème d’extension d’Ohsawa-Takegoshi. La même méthode donne une généralisation du théorème ∂ ¯ de Donnelly et Fefferman pour les formes de bidegré (n,1).

We give a short proof of the extension theorem of Ohsawa-Takegoshi. The same method also gives a generalization of the ∂ ¯-theorem of Donnelly and Fefferman for the case of (n,1)-forms.

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     title = {The extension theorem of {Ohsawa-Takegoshi} and the theorem of {Donnelly-Fefferman}},
     journal = {Annales de l'Institut Fourier},
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     volume = {46},
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Berndtsson, Bo. The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman. Annales de l'Institut Fourier, Tome 46 (1996) no. 4, pp. 1083-1094. doi : 10.5802/aif.1541. http://archive.numdam.org/articles/10.5802/aif.1541/

[A] E. Amar, Extension de fonctions holomorphes et courants, Bull. Sciences Mathématiques, 2ème série, 107 (1983), 25-48. | MR | Zbl

[Be1] B. Berndtsson, Weighted estimates for ∂ in domains in ℂ, Duke Math J., 66 (1992), 239-255. | MR | Zbl

[Be2] B. Berndtsson, Some recent results on estimates for the ∂-equation, in Contributions to Complex Analysis and Analytic Geometry, Eds. H. Skoda and J-M Trepreau, Vieweg, 1994. | MR | Zbl

[Be3] B. Berndtsson, Uniform estimates with weights for the ∂-equation, preprint 1994, to appear in J. Geom. Anal. | Zbl

[DH] K. Diederich and G Herbort, Extension of holomorphic L2-functions with weighted growth conditions, Nagoya Math. J., 126 (1992), 141-157. | MR | Zbl

[DOh] K. Diederich and T. Ohsawa, An estimate for the Bergman distance on pseudoconvex domains, Annals of Math., 141 (1995), 181-190. | MR | Zbl

[H] L. Hörmander, L2-estimates and existence theorems for the ∂-equation, Acta Math., 113 (1965). | Zbl

[KF] J. J. Kohn and G. Folland, The Neumann problem for the Cauchy-Riemann complex. | Zbl

[M] L. Manivel, Un théorème de prolongement L2 pour des sections holomorphes d'un fibré hermitien, Math. Z., 212 (1993), 107-122. | MR | Zbl

[McN] J. Mcneal, On large values of L2-holomorphic functions, Math. Res. Letters, 3 (1996), 247-260. | MR | Zbl

[OhT] T. Ohsawa and K. Takegoshi, On the extension of L2 holomorphic functions, Math. Z., 195 (1987), 197-204. | MR | Zbl

[S] Y-T Siu, The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi, preprint 1995. | Zbl

[S2] Y-T Siu, Complex-Analyticity at harmonic maps, vanishing and Lefschetz theorems, J. Diff. Geom., 17 (1982), 55-138. | MR | Zbl

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