Geometric conditions which imply compactness of the $\bar{\partial}$-Neumann operator

Details Geometric conditions which imply compactness of the $\bar{\partial}$-Neumann operator Geometric conditions which imply compactness of the $\bar{\partial}$-Neumann operator

2003-09-11

arxiv.org/abs/math/0309200v1

Mathematics

Complex Variables

10 pages

Scientific paper

For smooth bounded pseudoconvex domains in $mathbb{C}^{2}$, we provide
geometric conditions on (the points of infinite type in) the boundary which
imply compactness of the $\bar{\partial}$-Neumann operator. It is noteworthy
that the proof of compactness does \emph{not} proceed via verifying the known
potential theoretic sufficient conditions.

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