Displaying similar documents to “Smoothness of Cauchy Riemann maps for a class of real hypersurfaces.”

Behavior of holomorphic functions in complex tangential directions in a domain of finite type in C.

Sandrine Grellier (1992)

Publicacions Matemàtiques

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Let Ω be a domain in C. It is known that a holomorphic function on Ω behaves better in complex tangential directions. When Ω is of finite type, the best possible improvement is quantified at each point by the distance to the boundary in the complex tangential directions (see the papers on the geometry of finite type domains of Catlin, Nagel-Stein and Wainger for precise definition). We show that this improvement is characteristic: for a holomorphic function, a regularity in complex tangential...

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 ) ⊂ 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...

Local Peak Sets in Weakly Pseudoconvex Boundaries in ℂ n

Borhen Halouani (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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We give a sufficient condition for a C ω (resp. C ∞ )-totally real, complex-tangential, ( n - 1 ) -dimensional submanifold in a weakly pseudoconvex boundary of class C ω (resp. C ∞ ) to be a local peak set for the class 𝒪 (resp. A ∞ ). Moreover, we give a consequence of it for Catlin’s multitype.