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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.

Estimates of the Kobayashi-Royden metric in almost complex manifolds

Hervé Gaussier, Alexandre Sukhov (2005)

Bulletin de la Société Mathématique de France

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold ( M , J ) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in ( M , J ) .

Non compact boundaries of complex analytic varieties in Hilbert spaces

Samuele Mongodi, Alberto Saracco (2014)

Complex Manifolds

We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H.We deal with the problem by cutting with a family of complex hyperplanes and applying the already known result for the compact case.

On local geometry of finite multitype hypersurfaces

Martin Kolář (2007)

Archivum Mathematicum

This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in n + 1 . We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.

On the partial algebraicity of holomorphic mappings between two real algebraic sets

Joël Merker (2001)

Bulletin de la Société Mathématique de France

The rigidity properties of the local invariants of real algebraic Cauchy-Riemann structures imposes upon holomorphic mappings some global rational properties (Poincaré 1907) or more generally algebraic ones (Webster 1977). Our principal goal will be to unify the classical or recent results in the subject, building on a study of the transcendence degree, to discuss also the usual assumption of minimality in the sense of Tumanov, in arbitrary dimension, without rank assumption and for holomorphic...

Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Stephen S.-T. Yau (2011)

Journal of the European Mathematical Society

Let X 1 and X 2 be two compact strongly pseudoconvex CR manifolds of dimension 2 n - 1 5 which bound complex varieties V 1 and V 2 with only isolated normal singularities in N 1 and N 2 respectively. Let S 1 and S 2 be the singular sets of V 1 and V 2 respectively and S 2 is nonempty. If 2 n - N 2 - 1 1 and the cardinality of S 1 is less than 2 times the cardinality of S 2 , then we prove that any non-constant CR morphism from X 1 to X 2 is necessarily a CR biholomorphism. On the other hand, let X be a compact strongly pseudoconvex CR manifold of...

Un complément à l’article de Dloussky sur le colmatage des surfaces holomorphes

Marco Brunella (2008)

Annales de l’institut Fourier

Nous étudions les surfaces complexes compactes qui sont des dégénérations de surfaces de Hopf éclatées. Nous démontrons que si une telle surface S contient une hypersurface réelle globale strictement pseudoconvexe, alors S est une surface de Kato. Ceci permet d’améliorer un résultat de Dloussky, paru dans ce même journal en 1993.


Masanori Adachi, Judith Brinkschulte (0)

Annales de l’institut Fourier

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