Let be a pseudoconvex domain with C2 boundary in CP, n â‰¥ 2. We prove that the âˆ‚Ì„-Neumann operator N exists for square-integrable forms on . Furthermore, there exists a number 0 > 0 such that theâ€¦ (More)

The purpose of this note is to bring update results on boundary value problems on Lipschitz domains in R or C. We first discuss the Dirichlet problem, the Neumann problem and the d-Neumann problem inâ€¦ (More)

The âˆ‚Ì„b complex on the boundary of a complex manifold was first formulated by Kohn-Rossi [KR] to study the boundary values of holomorphic functions and holomorphic extensions. In this paper we studyâ€¦ (More)

We establish the L2 theory for the Cauchyâ€“Riemann equations on product domains provided that the Cauchyâ€“Riemann operator has closed range on each factor. We deduce regularity of the canonicalâ€¦ (More)

On a bounded pseudoconvex domain in C with a plurisubharmonic Lipschitz defining function, we prove that the âˆ‚Ì„-Neumann operator is bounded on Sobolev (1/2)-spaces. 0. Introduction Let D be a boundedâ€¦ (More)

Let X be a complex manifold. The study of the closed-range property of the CauchyRiemann equations is of fundamental importance both from the sheaf theoretic point of view and the PDE point of view.â€¦ (More)

In the Hilbert space approach, the closed range property for an unbounded closed operator characterizes the range of the operator. Thus it is important to know whether the range of an unboundedâ€¦ (More)

Let Mn be a complete, non-compact and Câˆž-smooth Riemannian manifold with nonnegative sectional curvature. Suppose S is a soul of Mn given by the fundamental theory of Cheeger and Gromoll, and supposeâ€¦ (More)

An L2 version of the Serre duality on domains in complex manifolds involving duality of Hilbert space realizations of the âˆ‚-operator is established. This duality is used to study the solution of theâ€¦ (More)