Displaying similar documents to “Some applications of a new integral formula for ∂ ̅ b ”

Tangential Cauchy-Riemann equations on quadratic manifolds

Marco M. Peloso, Fulvio Ricci (2002)

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

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We study the tangential Cauchy-Riemann equations ∂ ¯ b ⁢ u = ω for 0 , q -forms on quadratic C ⁢ R manifolds. We discuss solvability for data ω in the Schwartz class and describe the range of the tangential Cauchy-Riemann operator in terms of the signatures of the scalar components of the Levi form.

Decomposition of CR-manifolds and splitting of CR-maps

Atsushi Hayashimoto, Sung-Yeon Kim, Dmitri Zaitsev (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We show the uniqueness of local and global decompositions of abstract CR-manifolds into direct products of irreducible factors, and a splitting property for their CR-diffeomorphisms into direct products with respect to these decompositions. The assumptions on the manifolds are finite non-degeneracy and finite-type on a dense subset. In the real-analytic case, these are the standard assumptions that appear in many other questions. In the smooth case, the assumptions cannot be weakened...

Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree

Chin-Huei Chang, Hsuan-Pei Lee (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for C k ∂ ¯ -closed forms at the critical degree, 0 ≤ k ≤ ∞ (Theorem 1.1). Part of Frenkel’s lemma in C k category is also proved.