Extension De Germes De Difféomorphismes CR Pour Une Classe D'Hypersurfaces Analytiques Réelles Non Essentiellement Finies Dans C^3

Joel Merker (1) , Francine Meylan (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 UNIFR - Université de Fribourg = University of Fribourg

Let H: M --> M' be a germ of smooth CR diffeomorphism between M and M', two real analytic hypersurfaces at 0 in C^3, with M' given by Im w' = z_1'^mu \bar{z}_1'^mu \psi(z_1', \bar{z}_1', z_2', \bar{z}_2'), where \psi is a real analytic function in a neighborhood of 0 in C^2, satisfying \psi(0) \neq 0, \psi_{z_2^k}(0) \neq 0, for some k >= 1, \psi_{z_2'^\alpha \bar{z}_2'^\beta} = 0, for every choice of (\alpha, \beta) \in Z_+^* \times Z_+^*. We prove that His analytic.

Keywords: CR mappings; real analytic hypersurfaces; CR mappings; CR mappings

Domains: Mathematics [math]

Joel Merker, Francine Meylan. Extension De Germes De Difféomorphismes CR Pour Une Classe D'Hypersurfaces Analytiques Réelles Non Essentiellement Finies Dans C^3. Complex Variables and Elliptic Equations, 1999, 40 (1), pp.19-34. ⟨10.1080/17476939908815206⟩. ⟨hal-03285246⟩