Journal of the
Korean Mathematical Society JKMS

In this paper, we prove basic a priori estimate for the $\overline\partial$-Neumann problem on an annulus between two pseudoconvex submanifolds of a Stein manifold. As a corollary of the result, we obtain the global regularity for the $\overline\partial$-problem on the annulus. This is a manifold version of the previous results on pseudoconvex domains.

Keywords: Stein manifold, $\overline\partial$ and $\overline{\partial}$-Neumann operator, pseudoconvex domains

MSC numbers: 32F10, 32W05, 32W10