On the $L^2$-Dolbeault cohomology of annuli

DOI10.1512/iumj.2018.67.7307zbMath1414.32015arXiv1602.03896OpenAlexW2963873278MaRDI QIDQ4962385

Christine Laurent-Thiébaut, Debraj Chakrabarti, Mei-Chi Shaw

Publication date: 2 November 2018

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.03896

zbMATH Keywords

Dolbeault cohomologyannuli domainsdbar estimates

Mathematics Subject Classification ID

Analytic sheaves and cohomology groups (32C35) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Duality theorems for analytic spaces (32C37)

Related Items

Exact sequences and estimates for the \(\overline{\partial } \)-problem ⋮ Extendability and the \(\overline{\partial}\) operator on the Hartogs triangle ⋮ Hearing pseudoconvexity in Lipschitz domains with holes via \({\bar{\partial }}\) ⋮ On the Sobolev Dolbeault cohomology of a domain with pseudoconcave boundaries ⋮ Estimates for \(\overline{\partial}\) on domains in \(\mathbb{C}^n\) and \(\mathbb{CP}^n\) ⋮ On the canonical solution of \(\overline{\partial}\) on polydisks ⋮ A modified Morrey-Kohn-Hörmander identity and applications to the \(\overline{\partial}\)-problem ⋮ Percolation of estimates for \(\bar{\partial}\) by the method of alternating projections

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Hausdorff property of some Dolbeault cohomology groups
• The Cauchy-Riemann equations on product domains
• \(L^p\)-theory and Serre duality for the Cauchy-Riemann equation
• Some non-pseudoconvex domains with explicitly computable non-Hausdorff Dolbeault cohomology
• Holomorphy bundles and Hausdorff cohomology groups
• Solution of the \(\overline\partial\)-Neumann problem on a bi-disc
• Hearing pseudoconvexity with the Kohn Laplacian
• The null space of the \(\overline \partial \)-Neumann operator.
• Subelliptic estimates for the \(\overline\partial\)-Neumann operator on piecewise smooth strictly pseudoconvex domains
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• $L^{2}$ Serre duality on domains in complex manifolds and applications
• Cohomologie non abélienne et espaces fibrés
• Compactness of the $$\bar{\partial }$$-Neumann Operator on the Intersection of Two Domains
• Non-closed Range Property for the Cauchy-Riemann Operator
• Global Solvability and Regularity for $\overline\partial$ on an Annulus Between Two Weakly Pseudo-Convex Domains
• On the Infinite Dimensionality of the Dolbeault Cohomology Groups
• Global Regularity for $\overline \partial$ on Weakly Pseudo-Convex Manifolds
• Spectrum of the complex Laplacian on product domains
• On Serre Duality and Envelopes of Holomorphy
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
• On closed range for ∂̄