Displaying similar documents to “Levi-flat filling of real two-spheres in symplectic manifolds (I)”

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.

Immersed spheres in symplectic 4-manifolds

Dusa McDuff (1992)

Annales de l'institut Fourier

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We discuss conditions under which a symplectic 4-manifold has a compatible Kähler structure. The theory of J -holomorphic embedded spheres is extended to the immersed case. As a consequence, it is shown that a symplectic 4-manifold which has two different minimal reductions must be the blow-up of a rational or ruled surface.

Riemann maps in almost complex manifolds

Bernard Coupet, Hervé Gaussier, Alexandre Sukhov (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.

Holomorphic submersions from Stein manifolds

Franc Forstnerič (2004)

Annales de l’institut Fourier

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We establish the homotopy classification of holomorphic submersions from Stein manifolds to Complex manifolds satisfying an analytic property introduced in the paper. The result is a holomorphic analogue of the Gromov--Phillips theorem on smooth submersions.

Extending holomorphic mappings from subvarieties in Stein manifolds

Franc Forstneric (2005)

Annales de l’institut Fourier

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Suppose that Y is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space n to Y is a uniform limit of entire maps n Y . We prove that a holomorphic map X 0 Y from a closed complex subvariety X 0 in a Stein manifold X admits a holomorphic extension X Y provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.