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

Emil J. Straube

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

Emil J. Straube

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Abstract

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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Emil J. Straube. 2003-09-11. Geometric conditions which imply compactness of the $\bar{\partial}$-Neumann operator. https://arxiv.org/abs/math/0309200

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