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 -forms.
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 .
@article{AIF_1996__46_4_1083_0, author = {Berndtsson, Bo}, title = {The extension theorem of {Ohsawa-Takegoshi} and the theorem of {Donnelly-Fefferman}}, journal = {Annales de l'Institut Fourier}, pages = {1083--1094}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {4}, year = {1996}, doi = {10.5802/aif.1541}, mrnumber = {97k:32019}, zbl = {0853.32024}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1541/} }
TY - JOUR AU - Berndtsson, Bo TI - The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman JO - Annales de l'Institut Fourier PY - 1996 SP - 1083 EP - 1094 VL - 46 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1541/ DO - 10.5802/aif.1541 LA - en ID - AIF_1996__46_4_1083_0 ER -
%0 Journal Article %A Berndtsson, Bo %T The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman %J Annales de l'Institut Fourier %D 1996 %P 1083-1094 %V 46 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1541/ %R 10.5802/aif.1541 %G en %F AIF_1996__46_4_1083_0
Berndtsson, Bo. The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman. Annales de l'Institut Fourier, Volume 46 (1996) no. 4, pp. 1083-1094. doi : 10.5802/aif.1541. http://archive.numdam.org/articles/10.5802/aif.1541/
[A] Extension de fonctions holomorphes et courants, Bull. Sciences Mathématiques, 2ème série, 107 (1983), 25-48. | MR | Zbl
,[Be1] Weighted estimates for ∂ in domains in ℂ, Duke Math J., 66 (1992), 239-255. | MR | Zbl
,[Be2] 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] Uniform estimates with weights for the ∂-equation, preprint 1994, to appear in J. Geom. Anal. | Zbl
,[DH] Extension of holomorphic L2-functions with weighted growth conditions, Nagoya Math. J., 126 (1992), 141-157. | MR | Zbl
and ,[DOh] An estimate for the Bergman distance on pseudoconvex domains, Annals of Math., 141 (1995), 181-190. | MR | Zbl
and ,[H] L2-estimates and existence theorems for the ∂-equation, Acta Math., 113 (1965). | Zbl
,[KF] The Neumann problem for the Cauchy-Riemann complex. | Zbl
and ,[M] Un théorème de prolongement L2 pour des sections holomorphes d'un fibré hermitien, Math. Z., 212 (1993), 107-122. | MR | Zbl
,[McN] On large values of L2-holomorphic functions, Math. Res. Letters, 3 (1996), 247-260. | MR | Zbl
,[OhT] On the extension of L2 holomorphic functions, Math. Z., 195 (1987), 197-204. | MR | Zbl
and ,[S] The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi, preprint 1995. | Zbl
,[S2] Complex-Analyticity at harmonic maps, vanishing and Lefschetz theorems, J. Diff. Geom., 17 (1982), 55-138. | MR | Zbl
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