A class of domains with noncompact \overline{∂}-Neumann operator

The ∂ ¯ \overline {\partial } -Neumann operator (the inverse of the complex Laplacian) is shown to be noncompact on certain domains in complex Euclidean space. These domains are either higher-dimensional analogs of the Hartogs triangle or have such a generalized Hartogs triangle imbedded appropriately in them.