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arxiv: math/0309200 · v1 · submitted 2003-09-11 · 🧮 math.CV · math.AP

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

classification 🧮 math.CV math.AP
keywords compactnessconditionsgeometricimplyneumannoperatorpartialboundary
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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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