Geometric sufficient conditions for compactness of the complex Green operator

Abstract

We establish compactness estimates for ${\bar{\partial }}_M$ on a compact pseudoconvex CR-submanifold $M$ of ${\mathbb{C}}^n$ of hypersurface type that satisfies the (analogue of the) geometric sufficient conditions for compactness of the $\bar{\partial }$-Neumann operator given by the authors earlier. These conditions are formulated in terms of certain short time flows in complex tangential directions.

19 pages

References in corpus (3)

• Analytic discs, plurisubharmonic hulls, and non-compactness of the d-bar-Neumann operator
• A general method of weights in the d-bar-Neumann problem
• The complex Green operator on CR-submanifolds of ${\mathbb{C}}^n$ of hypersurface type: compactness