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We establish compactness estimates for $\bar{\partial}_{M}$ on a compactpseudoconvex CR-submanifold $M$ of $\mathbb{C}^{n}$ of hypersurface type thatsatisfies the (analogue of the) geometric sufficient conditions for compactnessof the $\bar{\partial}$-Neumann operator given by the authors earlier. Theseconditions are formulated in terms of certain short time flows in complextangential directions.

Geometric Sufficient Conditions for Compactness of the Complex Green Operator