- Tytuł:
- Non-solvability of the tangential ∂̅-system in manifolds with constant Levi rank
- Autorzy:
- Zampieri, Giuseppe
- Powiązania:
- https://bibliotekanauki.pl/articles/1207981.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
CR manifolds
∂̅ and $∂̅^b$ problems
tangential CR complex - Opis:
-
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. $s^{-}_{M} + s^{+}_{M} = n - codim M$). 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. - Źródło:
-
Annales Polonici Mathematici; 2000, 74, 1; 291-296
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł