Boundaries of Levi-flat hypersurfaces: special hyperbolic points

Abstract

Let $S\subset \C^n$, $n\ge 3$ 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. The particular cases of graphs are also described.

arXiv admin note: substantial text overlap with arXiv:1105.4417