Let S ⊂ ℂⁿ, n ≥ 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: a sphere with two horns, elementary models and their gluings. Some particular cases of S being a graph are also described.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-12,
author = {Pierre Dolbeault},
title = {Boundaries of Levi-flat hypersurfaces: special hyperbolic points},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {145-170},
zbl = {06100848},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-12}
}
Pierre Dolbeault. Boundaries of Levi-flat hypersurfaces: special hyperbolic points. Annales Polonici Mathematici, Tome 105 (2012) pp. 145-170. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-12/