Diederich-Fornaess theorem

Let $X\\subset{\\mathbb{C}}^{n}$ be a compact real analytic subvariety. Then $X$ containsno germ of a nontrivial complex analytic subvariety.

In particular, all compact real analytic subvarieties (or submanifolds) are D’Angelo finite type at every point.

References

1 M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild.,Princeton University Press,Princeton, New Jersey, 1999.
2 D’Angelo, John P.,CRC Press, 1993.
3 Klas Diederich,John E. Fornaess.Ann. Math. (2) 107 (1978), no. 2, 371–384.

单词	DiederichFornaessTheorem
释义	Diederich-Fornaess theorem Theorem (Diederich-Fornaes). Let $X\\subset{\\mathbb{C}}^{n}$ be a compact real analytic subvariety. Then $X$ containsno germ of a nontrivial complex analytic subvariety. In particular, all compact real analytic subvarieties (or submanifolds) are D’Angelo finite type at every point. References 1 M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild.,Princeton University Press,Princeton, New Jersey, 1999. 2 D’Angelo, John P.,CRC Press, 1993. 3 Klas Diederich,John E. Fornaess.Ann. Math. (2) 107 (1978), no. 2, 371–384.
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