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 .
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.
@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},
volume = {46},
year = {1996},
pages = {1083-1094},
doi = {10.5802/aif.1541},
mrnumber = {97k:32019},
zbl = {0853.32024},
language = {en},
url = {http://dml.mathdoc.fr/item/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, Tome 46 (1996) pp. 1083-1094. doi : 10.5802/aif.1541. http://gdmltest.u-ga.fr/item/AIF_1996__46_4_1083_0/
[A] , Extension de fonctions holomorphes et courants, Bull. Sciences Mathématiques, 2ème série, 107 (1983), 25-48. | MR 85c:32025 | Zbl 0543.32007
[Be1] , Weighted estimates for ∂ in domains in ℂ, Duke Math J., 66 (1992), 239-255. | MR 93f:32018 | Zbl 0774.35048
[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 96a:32035 | Zbl 0823.32007
[Be3] , Uniform estimates with weights for the ∂-equation, preprint 1994, to appear in J. Geom. Anal. | Zbl 0923.32014
[DH] and , Extension of holomorphic L2-functions with weighted growth conditions, Nagoya Math. J., 126 (1992), 141-157. | MR 93h:32016 | Zbl 0759.32002
[DOh] and , An estimate for the Bergman distance on pseudoconvex domains, Annals of Math., 141 (1995), 181-190. | MR 95j:32039 | Zbl 0828.32002
[H] , L2-estimates and existence theorems for the ∂-equation, Acta Math., 113 (1965). | Zbl 0158.11002
[KF] and , The Neumann problem for the Cauchy-Riemann complex. | Zbl 0247.35093
[M] , Un théorème de prolongement L2 pour des sections holomorphes d'un fibré hermitien, Math. Z., 212 (1993), 107-122. | MR 94e:32050 | Zbl 0789.32015
[McN] , On large values of L2-holomorphic functions, Math. Res. Letters, 3 (1996), 247-260. | MR 97e:32004 | Zbl 0865.32009
[OhT] and , On the extension of L2 holomorphic functions, Math. Z., 195 (1987), 197-204. | MR 88g:32029 | Zbl 0625.32011
[S] , The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi, preprint 1995. | Zbl 0941.32021
[S2] , Complex-Analyticity at harmonic maps, vanishing and Lefschetz theorems, J. Diff. Geom., 17 (1982), 55-138. | MR 83j:58039 | Zbl 0497.32025