The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman

Bo Berndtsson

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 4, page 1083-1094
  • ISSN: 0373-0956

Abstract

top
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.

How to cite

top

Berndtsson, Bo. "The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman." Annales de l'institut Fourier 46.4 (1996): 1083-1094. <http://eudml.org/doc/75200>.

@article{Berndtsson1996,
abstract = {We give a short proof of the extension theorem of Ohsawa-Takegoshi. The same method also gives a generalization of the $\bar\{\partial \}$-theorem of Donnelly and Fefferman for the case of $(n,1)$-forms.},
author = {Berndtsson, Bo},
journal = {Annales de l'institut Fourier},
keywords = {plurisubharmonic; pseudoconvex; },
language = {eng},
number = {4},
pages = {1083-1094},
publisher = {Association des Annales de l'Institut Fourier},
title = {The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman},
url = {http://eudml.org/doc/75200},
volume = {46},
year = {1996},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 4
SP - 1083
EP - 1094
AB - We give a short proof of the extension theorem of Ohsawa-Takegoshi. The same method also gives a generalization of the $\bar{\partial }$-theorem of Donnelly and Fefferman for the case of $(n,1)$-forms.
LA - eng
KW - plurisubharmonic; pseudoconvex;
UR - http://eudml.org/doc/75200
ER -

References

top
  1. [A] E. AMAR, Extension de fonctions holomorphes et courants, Bull. Sciences Mathématiques, 2ème série, 107 (1983), 25-48. Zbl0543.32007MR85c:32025
  2. [Be1] B. BERNDTSSON, Weighted estimates for ∂ in domains in ℂ, Duke Math J., 66 (1992), 239-255. Zbl0774.35048MR93f:32018
  3. [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. Zbl0823.32007MR96a:32035
  4. [Be3] B. BERNDTSSON, Uniform estimates with weights for the ∂-equation, preprint 1994, to appear in J. Geom. Anal. Zbl0923.32014
  5. [DH] K. DIEDERICH and G HERBORT, Extension of holomorphic L2-functions with weighted growth conditions, Nagoya Math. J., 126 (1992), 141-157. Zbl0759.32002MR93h:32016
  6. [DOh] K. DIEDERICH and T. OHSAWA, An estimate for the Bergman distance on pseudoconvex domains, Annals of Math., 141 (1995), 181-190. Zbl0828.32002MR95j:32039
  7. [H] L. HÖRMANDER, L2-estimates and existence theorems for the ∂-equation, Acta Math., 113 (1965). Zbl0158.11002
  8. [KF] J. J. KOHN and G. FOLLAND, The Neumann problem for the Cauchy-Riemann complex. Zbl0247.35093
  9. [M] L. MANIVEL, Un théorème de prolongement L2 pour des sections holomorphes d'un fibré hermitien, Math. Z., 212 (1993), 107-122. Zbl0789.32015MR94e:32050
  10. [McN] J. MCNEAL, On large values of L2-holomorphic functions, Math. Res. Letters, 3 (1996), 247-260. Zbl0865.32009MR97e:32004
  11. [OhT] T. OHSAWA and K. TAKEGOSHI, On the extension of L2 holomorphic functions, Math. Z., 195 (1987), 197-204. Zbl0625.32011MR88g:32029
  12. [S] Y-T SIU, The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi, preprint 1995. Zbl0941.32021
  13. [S2] Y-T SIU, Complex-Analyticity at harmonic maps, vanishing and Lefschetz theorems, J. Diff. Geom., 17 (1982), 55-138. Zbl0497.32025MR83j:58039

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.