Pierre Dolbeault
Boundaries of Levi-flat hypersurfaces: special hyperbolic points
Let $S\subset\mathbb C^n$, $n\geq3$, be a compact connected 2-codimensional submanifold having the following property: there exists a Levi-flat hypersurface whose boundary is $S$, possibly as a current. Our goal is to get examples of such $S$ containing at least one special 1-hyperbolic point: sphere with two horns; elementary models and their gluing.