Displaying similar documents to “Tangential Cauchy-Riemann equations on quadratic manifolds”

Some applications of a new integral formula for ∂ ̅ b

Moulay-Youssef Barkatou (1998)

Annales Polonici Mathematici

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Let M be a smooth q-concave CR submanifold of codimension k in ℂ n . We solve locally the ∂ ̅ b -equation on M for (0,r)-forms, 0 ≤ r ≤ q-1 or n-k-q+1 ≤ r ≤ n-k, with sharp interior estimates in Hölder spaces. We prove the optimal regularity of the ∂ ̅ b -operator on (0,q)-forms in the same spaces. We also obtain L p estimates at top degree. We get a jump theorem for (0,r)-forms (r ≤ q-2 or r ≥ n-k-q+1) which are CR on a smooth hypersurface of M. We prove some generalizations of the Hartogs-Bochner-Henkin...

Uniform estimates for the Cauchy-Riemann equation on q -convex wedges

Christine Laurent-Thiébaut, Jurgen Leiterer (1993)

Annales de l'institut Fourier

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We study the ∂ ‾ -equation with Hölder estimates in q -convex wedges of ℂ n by means of integral formulas. If D ⊂ ℂ n is defined by some inequalities { ρ i ≤ 0 } , where the real hypersurfaces { ρ i = 0 } are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the ρ i ’s have at least ( q + 1 ) positive eigenvalues, we solve the equation ∂ ‾ f = g for each continuous ( n , r ) -closed form g in D , n - q ≤ r ≤ n , with the following estimates: if d denotes the distance to the boundary of D and if d β g is bounded, then...

Non-solvability of the tangential ∂ ¯ M -systems

Giuseppe Zampieri (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove that for a real analytic generic submanifold M of C n whose Levi-form has constant rank, the tangential ∂ ¯ M -system is non-solvable in degrees equal to the numbers of positive and M negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with M non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.

The Poincaré lemma and local embeddability

Judith Brinkschulte, C. Denson Hill, Mauro Nacinovich (2003)

Bollettino dell'Unione Matematica Italiana

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For pseudocomplex abstract C ⁢ R manifolds, the validity of the Poincaré Lemma for 0 , 1 forms implies local embeddability in C N . The two properties are equivalent for hypersurfaces of real dimension ≥ 5 . As a corollary we obtain a criterion for the non validity of the Poicaré Lemma for 0 , 1 forms for a large class of abstract C ⁢ R manifolds of C ⁢ R codimension larger than one.