Abstract
We establish compactness estimates for \(\overline{\partial}_{M}\) on a compact pseudoconvex CR-submanifold M of ℂn of hypersurface type that satisfies the (analogue of the) geometric sufficient conditions for compactness of the \(\overline{\partial}\)-Neumann operator given in (Straube in Ann. Inst. Fourier, 54(3):699–710, 2004; Munasinghe and Straube in Pac. J. Math., 232(2):343–354 2007). These conditions are formulated in terms of certain short time flows in complex tangential directions.
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Communicated by Marco Abate.
Research supported in part by NSF grant DMS 0758534. This research was begun during a visit by the first author to the Department of Mathematics at Texas A&M University. She thanks the department for its hospitality.
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Munasinghe, S., Straube, E.J. Geometric Sufficient Conditions for Compactness of the Complex Green Operator. J Geom Anal 22, 1007–1026 (2012). https://doi.org/10.1007/s12220-011-9226-8
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DOI: https://doi.org/10.1007/s12220-011-9226-8
Keywords
- Complex Green operator
- CR-submanifold of hypersurface type
- \(\overline{\partial}_{b}\)
- Geometric conditions for compactness
- Complex tangential flow