Displaying similar documents to “Convergence of formal invertible CR mappings between minimal holomorphically nondegenerate real analytic hypersurfaces.”

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 ...

Unique determination of local C ⁢ R -maps by their jets: a survey

Dmitri Zaitsev (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We survey results on unique determination of local C ⁢ R -automorphisms of smooth C ⁢ R -manifolds and of local biholomorphisms of real-analytic C ⁢ R -submanifolds of complex spaces by their jets of finite order at a given point. Examples generalizing [28] are given showing that the required jet order may be arbitrarily high.

On Levi-flat hypersurfaces tangent to holomorphic webs

Arturo Fernández-Pérez (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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We investigate real analytic Levi-flat hypersurfaces tangent to holomorphic webs. We introduce the notion of first integrals for local webs. In particular, we prove that a k -web with finitely many invariant subvarieties through the origin tangent to a Levi-flat hypersurface has a holomorphic first integral.