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

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.

10 pages