New examples of non-locally embeddable $CR$ structures (with no non-constant $CR$ distributions)

Jean-Pierre Rosay

Displaying similar documents to “New examples of non-locally embeddable $C R$ structures (with no non-constant $C R$ distributions)”

Analytic extension from non-pseudoconvex boundaries and $A (D)$ -convexity

Christine Laurent-Thiébaut, Egmon Porten (2003)

Annales de l’institut Fourier

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Let $D \subset \subset ℂ^{n}, n \geq 2$ , be a domain with $C^{2}$ -boundary and $K \subset \partial D$ be a compact set such that $\partial D ∖ K$ is connected. We study univalent analytic extension of CR-functions from $\partial D ∖ K$ to parts of $D$ . Call $K$ CR-convex if its $A (D)$ -convex hull, $A (D) - hull (K)$ , satisfies $K = \partial D \cap A (D) - hull (K)$ ( $A (D)$ denoting the space of functions, which are holomorphic on $D$ and continuous up to $\partial D$ ). The main theorem of the paper gives analytic extension to $\partial D ∖ A (D) - hull (K)$ , if $K$ is CR- convex.

Maximum modulus sets

Thomas Duchamp, Edgar Lee Stout (1981)

Annales de l'institut Fourier

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We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain $D$ of dimension $N$ . If $Σ \subset b D$ is a smooth manifold of dimension $N$ and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in $A^{2} (D)$ with the same smooth $N$ -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in $H_{1} (D, R)$ vanishes or...

Envelopes of holomorphy in $ℂ^{2}$

Guido Lupacciolu (1999)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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 $M$ ...

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.

Displaying similar documents to “New examples of non-locally embeddable C R structures (with no non-constant C R distributions)”

Analytic extension from non-pseudoconvex boundaries and A ( D ) -convexity

Maximum modulus sets

Envelopes of holomorphy in ℂ 2

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

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

Displaying similar documents to “New examples of non-locally embeddable $C R$ structures (with no non-constant $C R$ distributions)”

Analytic extension from non-pseudoconvex boundaries and $A (D)$ -convexity

Envelopes of holomorphy in $ℂ^{2}$