Boundaries of Levi-flat hypersurfaces: special hyperbolic points

Tom 106 / 2012

Pierre Dolbeault Annales Polonici Mathematici 106 (2012), 145-170 MSC: Primary 32V40; Secondary 32V25, 32V15. DOI: 10.4064/ap106-0-12


Let $S\subset \mathbb C^n$, $n\geq 3$, 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: a sphere with two horns, elementary models and their gluings. Some particular cases of $S$ being a graph are also described.


  • Pierre DolbeaultInstitut de Mathématiques de Jussieu
    4, place Jussieu
    75005 Paris, France

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