Displaying similar documents to “Intersections of totally real and holomorphic disks.”

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.

Analytic disks with boundaries in a maximal real submanifold of 𝐂 2

Franc Forstneric (1987)

Annales de l'institut Fourier

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Let M be a two dimensional totally real submanifold of class C 2 in C 2 . A continuous map F : Δ C 2 of the closed unit disk Δ C into C 2 that is holomorphic on the open disk Δ and maps its boundary b Δ into M is called an analytic disk with boundary in M . Given an initial immersed analytic disk F 0 with boundary in M , we describe the existence and behavior of analytic disks near F 0 with boundaries in small perturbations of M in terms of the homology class of the closed curve F 0 ( b Δ ) in M . We also prove a regularity...

Partial indices of analytic discs attached to lagrangian submanifolds of N

Josip Globevnik (1996)

Annales de l'institut Fourier

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Integers κ 1 , ... , κ N are the partial indices of an analytic disc attached to a maximally real submanifolds of N if and only if κ j 2 for at least one j . If this is the case there are a Lagrangian submanifold M of N and an analytic disc attached to M with partial indices κ 1 , ... , κ N .

CR submanifolds of maximal CR dimension in complex manifolds

Mirjana Djorić, Masafumi Okumura (2002)

Banach Center Publications

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The aim of this paper is to investigate n-dimensional real submanifolds of complex manifolds in the case when the maximal holomorphic tangent space is (n-1)-dimensional. In particular, we give some examples and we consider the Levi form on these submanifolds, especially when the ambient space is a complex space form. Moreover, we show that on some remarkable class of real hypersurfaces of complex space forms, the Levi form cannot vanish identically.

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.