Cho, Hong Rae Global regularity of the \(\bar\partial\)-Neumann problem on an annulus between two pseudoconvex manifolds which satisfy property (P). (English) Zbl 0873.32013 Manuscr. Math. 90, No. 4, 437-448 (1996). 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 \(\Omega\). Reviewer: R.Salvi (Milano) Cited in 5 Documents MSC: 32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators 32T99 Pseudoconvex domains Keywords:\(\overline{\partial}\)-Neumann problem; pseudoconvex manifolds; Catlin condition PDFBibTeX XMLCite \textit{H. R. Cho}, Manuscr. Math. 90, No. 4, 437--448 (1996; Zbl 0873.32013) Full Text: DOI EuDML References: [1] Bell, S.: Biholomorphic mappings and the \(\overline \partial\) -problem, Ann. of Math.14, 103–113 (1981). · Zbl 0423.32009 · doi:10.2307/1971379 [2] Catlin, D.: Global regularity of the \(\overline \partial\) -Neumann problem. Proc. Symp. Pure Math.126, 39–49 (1984) [3] –: Subelliptic estimates for the \(\overline \partial\) -Neumann problem on pseudoconvex domains, Ann. of Math.126, 131–191 (1987) · Zbl 0627.32013 · doi:10.2307/1971347 [4] Derridj, M. and Fornaess, J. E.: Subelliptic estimate for the \(\overline \partial\) -Neumann problem, Duke Math. J.48, 93–107 (1981) · Zbl 0492.32019 · doi:10.1215/S0012-7094-81-04807-9 [5] Folland, G. B. and Kohn, J. J.: The Neumann problem for the Cauchy-Riemann complex, Ann. of Math. Studies, no. 75, Princeton Univ. Press, Princeton, N. J., 1972 · Zbl 0247.35093 [6] Hörmander, L.:L 2 estimates and existence theorems for the \(\overline \partial\) -operator, Acta Math.113, 89–152 (1965) · Zbl 0158.11002 · doi:10.1007/BF02391775 [7] Kohn, J.J.: Harmonic integrals on strongly pseudoconvex manifolds. I; II, Ann. of Math.78–2, 112–148 (1963);79–2, 450–472 (1964) · Zbl 0161.09302 · doi:10.2307/1970506 [8] – and Nirenberg, L.: Non-coercive boundary value problems, Comm. Pure Appl. Math.18, 443–492 (1965) · Zbl 0125.33302 · doi:10.1002/cpa.3160180305 [9] Kohn, J. J.: Global regularity for \(\overline \partial\) on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc.181, 273–292 (1873) · Zbl 0276.35071 [10] Krantz, S.: Compactness of the \(\overline \partial\) -Neumann operator, Proc. Amer. Math. Soc.103–4, 1136–1138 (1988) · Zbl 0736.35071 · doi:10.1090/S0002-9939-1988-0954995-2 [11] Shaw, M.-C.: Global solvability and regularity for \(\overline \partial\) on an annulus between two weakly pseudoconvex domains. Trans. Amer. Math. Soc.291–1, 255–267 (1985) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.