Global regularity of the \(\bar\partial\)-Neumann problem on an annulus between two pseudoconvex manifolds which satisfy property (P)
type: Item
instance of: scholarly article
title: Global regularity of the \(\bar\partial\)-Neumann problem on an annulus between two pseudoconvex manifolds which satisfy property (P)
zbMATH Open document ID: 0873.32013
DOI: 10.1007/BF02568317
author: Hong Rae Cho
published in: Manuscripta Mathematica
publication date: 1997-04-08T00:00:00Z
full work available at URL: https://eudml.org/doc/156204
review text: Let \(X\) be a complex manifold of dimension \(n\) and \(\Omega\Subset X\) be an open submanifold with smooth boundary. The paper concerns the \(\overline{\partial}\)-Neumann problem on \(\Omega\). The main result is Theorem. Let \(n\geq 3\). Let \(\Omega_1,\Omega_2\) be two open pseudoconvex manifolds with smooth boundary such that \(\Omega_1\Subset \Omega_2\Subset X\). Suppose that \(b\Omega_1\) and \(b\Omega_2\) satisfy the Catlin condition. Let \(\Omega= \Omega_2\setminus \overline{\Omega}_1\). Then the compactness estimate for \((p,q)\)-forms, \(0<q<n-1\) holds for the \(\overline{\partial}\)-Neumann problem on \(\Omega\).
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 980706
zbMATH Keywords: \(\overline{\partial}\)-Neumann problem
zbMATH Keywords: pseudoconvex manifolds
zbMATH Keywords: Catlin condition
reviewed by: Rodolfo Salvi
MaRDI profile type: Publication
cites work: Biholomorphic mappings and the \(\overline\partial\)-problem
cites work: Subelliptic estimates for the \({\bar \partial}\)-Neumann problem on pseudoconvex domains
cites work: Subelliptic estimate for the (partial d)-Neumann problem
cites work: The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
cites work: \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
cites work: Harmonic integrals on strongly pseudo-convex manifolds. I
cites work: Non‐coercive boundary value problems
cites work: Global Regularity for $\overline \partial$ on Weakly Pseudo-Convex Manifolds
cites work: Compactness of the $\overline\partial$-Neumann Operator
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description: scientific article; zbMATH DE number 980706