Holomorphic mappings between algebraic hypersurfaces in complex space

M. S. Baouendi; L. P. Rothschild

Displaying similar documents to “Holomorphic mappings between algebraic hypersurfaces in complex space”

On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions

Xiaojun Huang (1994)

Annales de l'institut Fourier

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In this paper, we show that if $M_{1}$ and $M_{2}$ are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if $f$ is a holomorphic mapping defined near a neighborhood of $M_{1}$ so that $f (M_{1}) \subset M_{2}$ , then $f$ is also algebraic. Our proof is based on a careful analysis on the invariant varieties and reduces to the consideration of many cases. After a slight modification, the argument is also used to prove a reflection principle, which allows our main result to be stated for...

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 $ℂ^{N + 1}$ , $N \geq 1$ , $M$ is not Levi-flat and $H$ is a germ at $p_{0}$ of a holomorphic mapping such that $H (M) \subseteq M^{'}$ 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...

Big Picard theorems for holomorphic mappings into the complement of $2 n + 1$ moving hypersurfaces in $ℂ P^{n}$ .

Nguyen Thi Thu Hang, Tran Van Tan (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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CR mappings between real hypersurfaces in complex space

M. S. Baouendi, L. P. Rothschild (1987-1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

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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 $M$ ...

CR mappings and their holomorphic extension

Mohamed S. Baouendi, Linda P. Rothschild (1987)

Journées équations aux dérivées partielles

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On holomorphic extension of functions on singular real hypersurfaces in $ℂ^{n}$ .

Neelon, Tejinder S. (2001)

International Journal of Mathematics and Mathematical Sciences

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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...