Abstract
Given a closed positive currentT on a bounded Runge open subset Ω ofC n, we study sufficient conditions for the existence of a global extension ofT toC n. WhenT 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 positiveC ∞-form outside\(\bar \Omega \). Conversely, using recent results ofH. Skoda andH. 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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Demailly, J. P., Courants positifs extrêmaux et conjecture de Hodge;Inv. Math.,69, (1982), 347–374.
Diederich, K. andFornaess, J. E., Smooth, but not complex analytic pluripolar sets;Manuscripta Math. 37, (1982), 121–125.
El Mir, H Théorèmes de prolongement des courants positifs fermés; Thèse de Doctorat d'Etat soutenue à l'Université de Paris VI, novembre 1982; Acta Math. 153 (1984).
Lelong, P.,Fonctions plurisousharmoniques et formes différentielles positives; Gordon and Breach, New York, et Dunod, Paris (1967).
Siu, Y. T., Analyticity of sets associated to Lelong numbers and the extension of closed positive currents;Inv. Math. 27, pp. 53–156 (1974).
Skoda, H., Prolongement des courants positifs fermés de masse finie;Inv. Math. 66, pp. 361–376 (1982).
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Demailly, JP. Propagation des singularités des courants positifs fermés. Ark. Mat. 23, 35–52 (1985). https://doi.org/10.1007/BF02384418
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DOI: https://doi.org/10.1007/BF02384418