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

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 ∞ -smooth CR diffeomorphism h : M → M ' between two globally minimal real analytic hypersurfaces in ℂ n ( n ≥ 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.