Observations regarding compactness in the $\overline{\partial}$-Neumann problem

Details Observations regarding compactness in the $\overline{\partial}$-Neumann problem Observations regarding compactness in the $\overline{\partial}$-Neumann problem

2008-06-23

arxiv.org/abs/0806.3783v1

Mathematics

Complex Variables

Scientific paper

We show that compactness of the $\overline{\partial}$-Neumann operator is independent of the metric, and we give a new proof of this independence for subellipticity. We define an abstract obstruction to compactness, namely the common zero set of all the compactness multipliers, and we identify this subset of the boundary for convex domains in $\mathbb{C}^{n}$ and for complete Hartogs domains in $\mathbb{C}^{2}$.

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