Singular set of a Levi-flat hypersurface is Levi-flat

Details Singular set of a Levi-flat hypersurface is Levi-flat Singular set of a Levi-flat hypersurface is Levi-flat

2010-12-29

arxiv.org/abs/1012.5993v2

Mathematics

Complex Variables

21 pages, improved exposition

Scientific paper

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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