Schwarz-type lemmas for solutions of $\bar{\partial }$-inequalities and complete hyperbolicity of almost complex manifolds

Sergey Ivashkovich; Jean-Pierre Rosay

Displaying similar documents to “Schwarz-type lemmas for solutions of $\bar{\partial}$ -inequalities and complete hyperbolicity of 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.

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.

On holomorphic maps into compact non-Kähler manifolds

Masahide Kato, Noboru Okada (2004)

Annales de l’institut Fourier

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We study the extension problem of holomorphic maps $σ : H \to X$ of a Hartogs domain $H$ with values in a complex manifold $X$ . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain $Ω_{σ}$ of extension for $σ$ over $Δ$ is contained in a subdomain of $Δ$ . For such manifolds, we define, in this paper, an invariant Hex $_{n} (X)$ using the Hausdorff dimensions of the singular sets of $σ$ ’s and study its properties to deduce informations on the complex structure of $X$ .

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 $ℂ^{n}$ to $Y$ is a uniform limit of entire maps $ℂ^{n} \to Y$ . We prove that a holomorphic map $X_{0} \to Y$ from a closed complex subvariety $X_{0}$ in a Stein manifold $X$ admits a holomorphic extension $X \to Y$ provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.

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 $𝒞^{\infty}$ -smooth CR diffeomorphism $h : M \to M^{'}$ between two globally minimal real analytic hypersurfaces in $ℂ^{n}$ ( $n \geq 2$ ) is real analytic at every point of $M$ ...

Displaying similar documents to “Schwarz-type lemmas for solutions of ∂ ¯ -inequalities and complete hyperbolicity of almost complex manifolds”

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

Holomorphic submersions from Stein manifolds

On holomorphic maps into compact non-Kähler manifolds

Extending holomorphic mappings from subvarieties in Stein manifolds

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

Displaying similar documents to “Schwarz-type lemmas for solutions of $\bar{\partial}$ -inequalities and complete hyperbolicity of almost complex manifolds”