Remarks on weakly pseudoconvex boundaries

Abstract

In this paper, we consider the boundary M of a weakly pseudoconvex domain in a Stein manifold. We point out a striking difference between the local cohomology and the global cohomology of M, and illustrate this with an example. We also discuss the first and second Cousin problems, and the strong Poincare problem for CR meromorphic functions on the weakly pseudoconvex boundary M.