Elliptic boundary value problem: Difference between revisions
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The '''Skoda–El Mir theorem''' is a theorem of [[complex geometry]], | |||
stated as follows: | |||
'''Theorem''' (Skoda,<ref>H. Skoda. ''Prolongement des courants positifs fermes de masse finie'', Invent. Math., 66 (1982), 361–376.</ref> El Mir,<ref>H. El Mir. ''Sur le prolongement des courants positifs fermes'', Acta Math., 153 (1984), 1–45.</ref> Sibony <ref>N. Sibony, ''Quelques problemes de prolongement de courants en analyse complexe,'' Duke Math. J., 52 (1985), 157–197</ref>). Let ''X'' be a [[complex manifold]], and | |||
''E'' a closed complete [[pluripolar set]] in ''X''. Consider a closed [[positive current]] <math>\Theta</math> on <math> X \backslash E</math> | |||
which is locally integrable around ''E''. Then the trivial extension of <math>\Theta</math> to ''X'' is closed on ''X''. | |||
==Notes== | |||
<references /> | |||
==References== | |||
*J.-P. Demailly,'' [http://arxiv.org/abs/alg-geom/9410022 L² vanishing theorems for positive line bundles and adjunction theory, Lecture Notes of a CIME course on "Transcendental Methods of Algebraic Geometry" (Cetraro, Italy, July 1994)]'' | |||
{{DEFAULTSORT:Skoda-El Mir theorem}} | |||
[[Category:Complex manifolds]] | |||
[[Category:Several complex variables]] | |||
[[Category:Theorems in geometry]] | |||
{{differential-geometry-stub}} | |||
Latest revision as of 15:52, 11 December 2013
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