Abstract
Given a closed positive current T on a bounded Runge open subset Ω of ℂ2, we study sufficient conditions for the existence of a global extension of T to ℂ2. When T has a sufficiently low density, we show that the extension exists 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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© 1984 Springer-Verlag
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Demailly, JP. (1984). Sur la propagation des singularites des courants positifs fermes. In: Amar, E., Gay, R., Van Thanh, N. (eds) Analyse Complexe. Lecture Notes in Mathematics, vol 1094. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099155
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DOI: https://doi.org/10.1007/BFb0099155
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