# Extension of L^2, di-bar-closed, forms

@article{Baracco2015ExtensionOL, title={Extension of L^2, di-bar-closed, forms}, author={Luca Baracco and Stefano Pinton and Giuseppe Zampieri}, journal={arXiv: Complex Variables}, year={2015} }

We prove extension of a di-bar-closed, smooth, form from the intersection of a pseudoconvex domain with a complex hyperplane to the whole domain. The extension form is di-bar-closed, has harmonic coefficients and its L^2-norm is estimated by the L^2-norm of the trace. For holomorphic functions this is proved by Ohsawa-Takegoshi [12]. For forms of higher degree, this is stated by Manivel [9]. It seems, however, that the proof contains a gap because of the use of a a singular weight and the…

## One Citation

### $$L^2$$ Extension of $${{\bar{\partial }}}$$-Closed Forms on Weakly Pseudoconvex Kähler Manifolds

- MathematicsThe Journal of Geometric Analysis
- 2022

Combining V. Koziarz's observation about the regularity of some modified section related to the initial extension with J. McNeal--D. Varolin's regularity argument, we generalize two theorems of…

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© Annales de l’institut Fourier, 1996, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions…