# Levi-flat hypersurfaces with real analytic boundary

@article{Lebl2007LeviflatHW, title={Levi-flat hypersurfaces with real analytic boundary}, author={Jiř{\'i} Lebl}, journal={Transactions of the American Mathematical Society}, year={2007}, volume={362}, pages={6367-6380} }

Let X be a Stein manifold of dimension at least 3. Given a compact codimension 2 real analytic submanifold M of X, that is the boundary of a compact Levi-flat hypersurface H, we study the regularity of H. Suppose that the CR singularities of M are an O(X)-convex set. For example, suppose M has only finitely many CR singularities, which is a generic condition. Then H must in fact be a real analytic submanifold. If M is real algebraic, it follows that H is real algebraic and in fact extends past…

## 2 Citations

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

- Mathematics
- 2013

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…

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