# Elliptic boundary value problem

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*.

## Notes

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