Global regularity of the \(\bar\partial\)-Neumann problem on an annulus between two pseudoconvex manifolds which satisfy property (P) (Q1352987)

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 \(\Omega\).