SOLUTION TO $\overline{\partial}$-EQUATIONS WITH EXACT SUPPORT ON PSEUDO-CONVEX MANIFOLDS

DOI10.1142/S0219887807002090zbMath1142.32020OpenAlexW2117932221MaRDI QIDQ3502869

Osama Abdelkader, Sayed Saber

Publication date: 20 May 2008

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219887807002090

zbMATH Keywords

\(\overline\partial\)-equationNeumann operatorpseudo convex domains

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Extension of functions and other analytic objects from CR manifolds (32V25) (overlinepartial_b) and (overlinepartial_b)-Neumann operators (32W10)

Related Items (6)

On the Applications of Bochner-Kodaira-Morrey-Kohn Identity ⋮ SOLUTION TO $\overline{\partial}$ PROBLEM WITH EXACT SUPPORT AND REGULARITY FOR THE $\overline{\partial}$-NEUMANN OPERATOR ON WEAKLY q-CONVEX DOMAINS ⋮ The L 2 $$\overline \partial $$ -Cauchy problem on weakly q-pseudoconvex domains in Stein manifolds ⋮ Unnamed Item ⋮ Solvability of the tangential Cauchy-Riemann equations on boundaries of strictly \(q\)-convex domains ⋮ Unnamed Item

Cites Work

• Régularité pour \(\overline\partial\) dans quelques domaines faiblement pseudo-convexes
• Local existence theorems with estimates for \(\bar \partial_ b\) on weakly pseudo-convex CR manifolds
• Compactness of the Neumann operator for hyperconvex domains with non-smooth \(B\)-regular boundary
• Estimates for the \(\bar\partial\)-Neumann problem and nonexistence of \(C^2\) Levi-flat hypersurfaces in \(\mathbb{C} P^n\)
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• On the extension of holomorphic functions from the boundary of a complex manifold

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