Boundaries of Levi-flat hypersurfaces: special hyperbolic points

TL;DR

This paper explores the boundaries of Levi-flat hypersurfaces in complex spaces, providing examples with special hyperbolic points, including models, their gluing, and cases involving graphs.

Contribution

It introduces new examples of boundaries with hyperbolic points for Levi-flat hypersurfaces, expanding understanding of their geometric and topological properties.

Findings

Constructed examples with special hyperbolic points

Described elementary models and their gluings

Analyzed cases involving graphs of hypersurfaces

Abstract

Let $S\subset \C^n$, $n\geq 3$ 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.