Singular set of a Levi-flat hypersurface is Levi-flat
Jiri Lebl
TL;DR
This paper investigates the structure of singular Levi-flat hypersurfaces, proving their singular sets are Levi-flat and that under certain conditions, Levi-foliations extend holomorphically.
Contribution
It establishes that the singular set of a Levi-flat hypersurface is Levi-flat and extends Levi-foliations holomorphically when the singular set is sufficiently small.
Findings
Singular set of Levi-flat hypersurface is Levi-flat.
Levi-foliation extends holomorphically under small singular set.
Provides conditions for extension of Levi-foliations.
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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