Displaying similar documents to “On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions”

Germs of holomorphic mappings between real algebraic hypersurfaces

Nordine Mir (1998)

Annales de l'institut Fourier

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We study germs of holomorphic mappings between general algebraic hypersurfaces. Our main result is the following. If ( M , p 0 ) and ( M ' , p 0 ' ) are two germs of real algebraic hypersurfaces in ℂ N + 1 , N ≥ 1 , M is not Levi-flat and H is a germ at p 0 of a holomorphic mapping such that H ( M ) ⊆ M ' and Jac ( H ) ≢ 0 then the so-called reflection function associated to H is always holomorphic algebraic. As a consequence, we obtain that if M ' is given in the so-called normal form, the transversal component of H is always algebraic. Another...

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

Joël Merker (2001)

Bulletin de la Société Mathématique de France

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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...

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 ...

Smoothness of Cauchy Riemann maps for a class of real hypersurfaces.

Hervé Gaussier (2001)

Publicacions Matemàtiques

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We study the regularity problem for Cauchy Riemann maps between hypersurfaces in C. We prove that a continuous Cauchy Riemann map between two smooth C pseudoconvex decoupled hypersurfaces of finite D'Angelo type is of class C.