Singular set of a Levi-flat hypersurface is Levi-flat
classification
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math.DS
keywords
singularhypersurfacelevi-flatappropriatecodimensionenoughextendsfoliation
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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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