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Boundaries of Levi-flat hypersurfaces: special hyperbolic points

Pierre Dolbeault (2012)

Annales Polonici Mathematici

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.

Bounded symmetric domains and derived geometric structures

Wilhelm Kaup (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Every homogeneous circular convex domain D C n (a bounded symmetric domain) gives rise to two interesting Lie groups: The semi-simple group G = A u t D of all biholomorphic automorphisms of D and its isotropy subgroup K G L n , C at the origin (a maximal compact subgroup of G ). The group G acts in a natural way on the compact dual X of D (a certain compactification of C n that generalizes the Riemann sphere in case D is the unit disk in C ). Various authors have studied the orbit structure of the G -space X , here we are interested...

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