Abstract
Given a closed positive current T on a bounded Runge open subset Ω of Cn, we study sufficient conditions for the existence of a global extension of T to Cn. 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).
Citation
Jean-Pierre Demailly. "Propagation des singularités des courants positifs fermés." Ark. Mat. 23 (1-2) 35 - 52, 1985. https://doi.org/10.1007/BF02384418
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