# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc: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).
@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.