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Fonctions et feuilletages Levi-Flat. Étude locale

Dominique Cerveau, Paulo R. Sad (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.

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

Joël Merker (2002)

Annales de l’institut Fourier

In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function 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 n ( n 2 ) is real analytic at every point...

On the partial algebraicity of holomorphic mappings between two real algebraic sets

Joël Merker (2001)

Bulletin de la Société Mathématique de France

The rigidity properties of the local invariants of real algebraic Cauchy-Riemann structures imposes upon holomorphic mappings some global rational properties (Poincaré 1907) or more generally algebraic ones (Webster 1977). Our principal goal will be to unify the classical or recent results in the subject, building on a study of the transcendence degree, to discuss also the usual assumption of minimality in the sense of Tumanov, in arbitrary dimension, without rank assumption and for holomorphic...

The holomorphic extension of C k CR functions on tube submanifolds

Al Boggess (1998)

Annales Polonici Mathematici

We show that a CR function of class C k , 0 ≤ k < ∞, on a tube submanifold of n holomorphically extends to the convex hull of the submanifold. The extension and all its derivatives through order k are shown to have nontangential pointwise boundary values on the original tube submanifold. The C k -norm of the extension is shown to be no bigger than the C k -norm of the original CR function.

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

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.

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