Elliptic boundary value problem

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The Skoda–El Mir theorem is a theorem of complex geometry, stated as follows:

Theorem (Skoda,[1] El Mir,[2] Sibony [3]). Let X be a complex manifold, and E a closed complete pluripolar set in X. Consider a closed positive current on which is locally integrable around E. Then the trivial extension of to X is closed on X.


  1. H. Skoda. Prolongement des courants positifs fermes de masse finie, Invent. Math., 66 (1982), 361–376.
  2. H. El Mir. Sur le prolongement des courants positifs fermes, Acta Math., 153 (1984), 1–45.
  3. N. Sibony, Quelques problemes de prolongement de courants en analyse complexe, Duke Math. J., 52 (1985), 157–197