Boundary regularity for thebar partial _b - Neumann problem, part 1problem, part 1

We establish sharp regularity and Fredholm theorems for the operator on domains satisfying some nongeneric geometric conditions. We use these domains to construct explicit examples of bad behavior of the Kohn Laplacian: It is not always hypoelliptic up to the boundary, its partial inverse is not compact and it is not globally subelliptic.