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

Giuseppe Zampieri (2000)

Annales Polonici Mathematici

Let M be a real-analytic submanifold of 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....

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