A transversal Fredholm property for the $\bar\partial$-Neumann problem on $G$-bundles

Abstract

Let $M$ be a strongly pseudoconvex complex $G$-manifold with compact quotient $M/G$. We provide a simple condition on forms $\alpha$ sufficient for the regular solvability of the equation $\square u=\alpha$ and other problems related to the $\bar\partial$-Neumann problem on $M$.