Remarks on weakly pseudoconvex boundaries

TL;DR

This paper investigates the properties of weakly pseudoconvex boundaries in Stein manifolds, highlighting differences in local and global cohomology, and exploring classical complex analysis problems on these boundaries.

Contribution

It reveals a notable difference between local and global cohomology on weakly pseudoconvex boundaries and discusses classical problems like Cousin and Poincare problems in this context.

Findings

Difference between local and global cohomology demonstrated

Example illustrating cohomology discrepancy provided

Analysis of classical complex analysis problems on 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.