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Compactness of the complex Green operator on non-pseudoconvex CR manifolds

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This work was supported by a grant from the Simons Foundation (707123, ASR)
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  • In this paper, we investigate the compactness theory of the complex Green operator on smooth, embedded, orientable CR manifolds of hypersurface type that satisfy the weak $ Y(q) $ condition. The sufficient condition that we define is an adaption of the CR-$ P_q $ property for weak $ Y(q) $ manifolds and does not require that the CR manifold is the boundary of a domain.

    We also provide several non-pseudoconvex examples (and a level $ q $) for which the complex Green operator is compact.

    Mathematics Subject Classification: Primary: 32W10, Secondary: 32F17, 32V20, 35A27, 35N15.


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