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Propagation des singularités des courants positifs fermés

Jean-Pierre Demailly Laboratoire de Mathématiques Pures-Institut Fourier dépendant de l'Université Scientifique et Médicale de Grenoble, associé au C.N.R.S.

TBD mathscidoc:1701.332614

Arkiv for Matematik, 23, (1), 35-52, 1983.7
Given a closed positive current$T$on a bounded Runge open subset Ω of$C$^{$n$}, we study sufficient conditions for the existence of a global extension of$T$to$C$^{$n$}. When$T$has a sufficiently low density, we show that the extension is possible and that there is no propagation of singularities, i.e.$T$may be extended by a closed positive$C$^{∞}-form outside $$\bar \Omega $$ . Conversely, using recent results of$H.$Skoda and$H.$El Mir, we give examples of non extendable currents showing that the above sufficient conditions are optimal in bidegree (1, 1).
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@inproceedings{jean-pierre1983propagation,
  title={Propagation des singularités des courants positifs fermés},
  author={Jean-Pierre Demailly},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203519065266423},
  booktitle={Arkiv for Matematik},
  volume={23},
  number={1},
  pages={35-52},
  year={1983},
}
Jean-Pierre Demailly. Propagation des singularités des courants positifs fermés. 1983. Vol. 23. In Arkiv for Matematik. pp.35-52. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203519065266423.
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