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

Chakrabarti, Debraj

doi:10.1090/S0002-9939-2013-11504-2

A class of domains with noncompact $\overline {\partial }$-Neumann operator
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Proc. Amer. Math. Soc. 141 (2013), 2351-2359 Request permission

Abstract:

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.

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