相关论文: Filling hypersurfaces by discs in almost complex m…

We study pseudoholomorphic discs with boundaries attached to a real hypersurface in an almost complex manifold. We give sufficient conditions for filling a one sided neighborhood of the hypersurface by the discs.

Let E be a generic real submanifold of an almost complex manifold. The geometry of Bishop discs attached to E is studied in terms of the Levi form of E.

We prove the existence and study the geometry of Bishop discs near an elliptic point of a real n-dimensional submanifold of an almost complex n-dimensional manifold.

For a given embedded Lagrangian in the complement of a complex hypersurface we show existence of a holomorphic disc in the complement having boundary on that Lagrangian.

We provide a local approximation result of non-holomorphic discs with small d-bar by pseudoholomorphic ones. As an application, we provide a certain gluing construction.

We prove the existence of global Bishop discs in a strictly pseudoconvex Stein domain in an almost complex manifold of complex dimension 2.

Let $D=\{\rho<0\}$ be a smooth domain of finite type in an almost complex manifold (M,J) of real dimension four. We assume that the defining function $\rho$ is J-plurisubharmonic on a neighborhood of $\overline{D}$. We study the asymptotic…

Let X be a complex manifold of dimension at least 2 which has an exhaustion function whose Levi form has at each point at least 2 positive eigenvalues. We prove that there are proper holomorphic discs in X through any given point

In this paper we extend the notion of the Kobayashi-Royden pseudonorm for almost complex manifolds. Its basic properties known from the complex analysis are preserved in the nonintegrable case as well. The main theorem on coincidence of the…

We prove that there are no pseudoholomorphic theories of anything other than curves, even if one allows more general spaces than almost complex manifolds. The proof is elementary, except for theories of pseudoholomorphic hypersurfaces,…

We prove that for any complex manifold X, the set of all holomorphic maps from the unit disc to X whose images are everywhere dense in X forms a dense subset in the space of all holomorphic maps from the disc to X. We show by an example…

We study the existence of topologically closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any noncompact complex space admitting an exhaustion function whose Levi…

We construct a finitely dimensional invariant manifold of holomorphic discs attached to a certain class of smooth pseudconvex hypersurfaces of finite type in $\C^2$, generalizing the notion of stationary discs. The discs we construct are…

We give a necessary and sufficient condition for the existence of nondegenerate holomorphic mappings between pseudoellipsoidal real hypersurfaces, and provide an explicit parametrization for the collection of all such mappings (in the…

We prove that pseudo-holomorphic discs attached to a maximal totally real submanifold inherit their regularity from the regularity of the submanifold and of the almost complex structure. The proof is based on the computation of an explicit…

The envelope of holomorphy of an arbitrary domain in a two-dimensional Stein manifold is identified with a connected component of the set of equivalence classes of analytic discs immersed into the Stein manifold with boundary in the domain.…

We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.

We prove analogs of Thom's transversality theorem and Whitney's theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a manifold.

In this paper, we first prove that the totally real discs lying in certain Levi flat hypersurfaces are polynomially convex. As applications we prove that the totally real discs lying in the boundary of certain polynomial polyhedra are…

This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…