Abstract
We prove that the tangential Cauchy–Riemann operator \({\bar{\partial }}_b\) has closed range on Levi-pseudoconvex CR manifolds that are embedded in a q-convex complex manifold X. Our result generalizes the known case when X is a Stein manifold (in particular, when \(X={\mathbb C}^n\)).
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Acknowledgements
The authors would like to thank Martino Fassina for useful comments on the manuscript and the anonymous referee whose advice improved greatly the expository quality of the paper.
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Research of the Alexander Tumanov is partially supported by Simons Foundation Grant.
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To the memory of Nicholas Hanges.
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Baracco, L., Tumanov, A. A note on the closed range of \({\bar{\partial }}_b\) on q-convex manifolds. Complex Anal Synerg 6, 14 (2020). https://doi.org/10.1007/s40627-020-00053-w
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DOI: https://doi.org/10.1007/s40627-020-00053-w