Non-solvability of the tangential ∂̅-system in manifolds with constant Levi rank

Giuseppe Zampieri

Annales Polonici Mathematici, Tome 75 (2000), p. 291-296 / Harvested from The Polish Digital Mathematics Library

Résumé

Let M be a real-analytic submanifold of $ℂ^{n}$ whose “microlocal” Levi form has constant rank $s_{M}^{+} + s_{M}^{-}$ in a neighborhood of a prescribed conormal. Then local non-solvability of the tangential ∂̅-system is proved for forms of degrees $s_{M}^{-}$ , $s_{M}^{+}$ (and 0). This phenomenon is known in the literature as “absence of the Poincaré Lemma” and was already proved in case the Levi form is non-degenerate (i.e. $s_{M}^{-} + s_{M}^{+} = n - c o d i m M$ ). We owe its proof to [2] and [1] in the case of a hypersurface and of a higher-codimensional submanifold respectively. The idea of our proof, which relies on the microlocal theory of sheaves of [3], is new.

Publié le : 2000-01-01

Zbl 0967.32037

EUDML-ID : urn:eudml:doc:208373

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     author = {Giuseppe Zampieri},
     title = {Non-solvability of the tangential [?]-system in manifolds with constant Levi rank},
     journal = {Annales Polonici Mathematici},
     volume = {75},
     year = {2000},
     pages = {291-296},
     zbl = {0967.32037},
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Giuseppe Zampieri. Non-solvability of the tangential ∂̅-system in manifolds with constant Levi rank. Annales Polonici Mathematici, Tome 75 (2000) pp. 291-296. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv74z1p291bwm/

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