Regularity of \(\overline{\partial}\) on pseudoconcave compacts and applications

DOI10.4310/AJM.2000.v4.n4.a9zbMath0998.32021OpenAlexW2687740081MaRDI QIDQ5947041

Gennadi M. Henkin, Andrei Iordan

Publication date: 17 November 2002

Published in: The Asian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/ajm.2000.v4.n4.a9

zbMATH Keywords

cohomology groups\(\bar\partial\)-equationHartogs-Bochner TheoremLipschitz domainspseudoconcave domainsvanishing of the cohomology groups

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) (q)-convexity, (q)-concavity (32F10) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Vanishing theorems (32L20)

Related Items (16)

On the Applications of Bochner-Kodaira-Morrey-Kohn Identity ⋮ The \(\bar \partial\)-problem with support conditions on some weakly pseudoconvex domains ⋮ Global boundary regularity for the \(\overline\partial\)-problem on strictly \(q\)-convex and \(q\)-concave domains ⋮ The \(\bar\partial\)-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in \(\mathbb{C}P^n\) with \(n \geq 3\) ⋮ Regularity of the \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\overline{\partial }}$\end{document}-equation and Liouville's theorem for pseudoconcave compacts in \documentclass{article}\usepackage{amssymb}\begin{document} ⋮ The L2 ∂¯-Cauchy problem on pseudoconvex domains and applications ⋮ On \(L^2\)-estimates for \(\overline{\partial}\) on pseudoconvex domains in a complete Kähler manifold with positive holomorphic bisectional curvature ⋮ Hartogs-Bochner type theorem in projective space ⋮ On \(L^2\)-estimates for \(\bar\partial\) on a pseudoconvex domain in a complete Kähler manifold with positive holomorphic bisectional curvature ⋮ Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle ⋮ On the Levi-flats in complex tori of dimension two ⋮ Bounded plurisubharmonic exhaustion functions and Levi-flat hypersurfaces ⋮ Curvature restrictions for Levi-flat real hypersurfaces in complex projective planes ⋮ Nonexistence of Levi flat hypersurfaces with positive normal bundle in compact Kähler manifolds of dimension ≥3 ⋮ On weighted Bergman spaces of a domain with Levi-flat boundary ⋮ Unnamed Item

This page was built for publication: Regularity of \(\overline{\partial}\) on pseudoconcave compacts and applications