Abstract
We study the singular set of a singular Levi-flat real-analytic hypersurface. We prove that the singular set of such a hypersurface is Levi-flat in the appropriate sense. We also show that if the singular set is small enough, then the Levi-foliation extends to a singular codimension one holomorphic foliation of a neighborhood of the hypersurface.
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Acknowledgments
The author would like to acknowledge Peter Ebenfelt for suggesting the study of this problem when the author was still a graduate student, and also for many conversations on the topic. The author would also like to thank Xianghong Gong, John P. D’Angelo, Salah Baouendi, Linda Rothschild, and Arturo Fernández-Pérez for fruitful discussions on topics related to this research and suggestions on the manuscript.
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J. Lebl was in part supported by NSF grant DMS 0900885.
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Lebl, J. Singular set of a Levi-flat hypersurface is Levi-flat. Math. Ann. 355, 1177–1199 (2013). https://doi.org/10.1007/s00208-012-0821-1
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DOI: https://doi.org/10.1007/s00208-012-0821-1