Displaying similar documents to “Riemann maps in almost complex manifolds”

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.

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 complete intersections

Franc Forstnerič (2001)

Annales de l’institut Fourier

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We construct closed complex submanifolds of ℂ n which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of ℂ n .

Embeddability of abstract CR structures and integrability of related systems

Salah Baouendi, Linda P. Rothschild (1987)

Annales de l'institut Fourier

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Necessary and sufficient conditions for local embeddability of abstract C R structures are expressed in terms of the commutation of the C R vector fields with a complex Lie algebra. These results extend to more general systems.

Failure of averaging on multiply connected domains

David E. Barrett (1990)

Annales de l'institut Fourier

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We show that for every open Riemann surface X with non-abelian fundamental group there is a multiple-valued function f on X such that the fiberwise convex hull of the graph of f fails to contain the graph of a single-valued holomorphic function on X .