Displaying similar documents to “Levi flat hypersurfaces in C 2 with prescribed boundary : stability”

Levi-flat filling of real two-spheres in symplectic manifolds (II)

Hervé Gaussier, Alexandre Sukhov (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider a compact almost complex manifold ( M , J , ω ) with smooth Levi convex boundary ∂ M and a symplectic tame form ω . Suppose that S 2 is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into ∂ M . We prove a result on filling S 2 by holomorphic discs.

Boundaries of Levi-flat hypersurfaces: special hyperbolic points

Pierre Dolbeault (2012)

Annales Polonici Mathematici

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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.

Levi-flat filling of real two-spheres in symplectic manifolds (I)

Hervé Gaussier, Alexandre Sukhov (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let ( M , J , ω ) be a manifold with an almost complex structure J tamed by a symplectic form ω . We suppose that M has the complex dimension two, is Levi-convex and with bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of M can be foliated by the boundaries of pseudoholomorphic discs.

Maximum modulus sets and reflection sets

Alexander Nagel, Jean-Pierre Rosay (1991)

Annales de l'institut Fourier

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We study sets in the boundary of a domain in C n , on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to , which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.

Schwarz-type lemmas for solutions of ∂ ¯ -inequalities and complete hyperbolicity of almost complex manifolds

Sergey Ivashkovich, Jean-Pierre Rosay (2004)

Annales de l'Institut Fourier

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The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.

On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle

Joël Merker (2002)

Annales de l’institut Fourier

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In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat “hat”. In our main theorem, we show that every 𝒞 ∞ -smooth CR diffeomorphism h : M → M ' between two globally minimal real analytic hypersurfaces in ℂ n ( n ≥ 2 ) is real analytic at every point of M ...