A Class of Domains with noncompact $\bar{\partial}$-Neumann operator
  The $\bar{\partial}$-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. 
Debraj Chakrabarti
math.CV