Real Analyticity of Homeomorphic CR Mappings Between Real Analytic Hypersurfaces in C 2

1995 ◽  
Vol 123 (2) ◽  
pp. 373 ◽  
Author(s):  
Yifei Pan
Keyword(s):  
Cr Mappings ◽  
Real Analyticity ◽  
Real Analytic ◽  
Real Analytic Hypersurfaces

scholarly journals Convergence of formal invertible CR mappings between minimal holomorphically nondegenerate real analytic hypersurfaces

2001 ◽  
Vol 26 (5) ◽  
pp. 281-302 ◽  
Author(s):  
Joël Merker
Keyword(s):  
Forthcoming Paper ◽  
Holomorphic Mappings ◽  
Optimal Regularity ◽  
Cr Manifolds ◽  
Cr Mappings ◽  
Algebraic Sets ◽  
Riemann Geometry ◽  
Recent Advances ◽  
Real Analytic ◽  
Real Analytic Hypersurfaces

Recent advances in CR (Cauchy-Riemann) geometry have raised interesting fine questions about the regularity of CR mappings between real analytic hypersurfaces. In analogy with the known optimal results about the algebraicity of holomorphic mappings between real algebraic sets, some statements about the optimal regularity of formal CR mappings between real analytic CR manifolds can be naturally conjectured. Concentrating on the hypersurface case, we show in this paper that a formal invertible CR mapping between two minimal holomorphically nondegenerate real analytic hypersurfaces inℂnis convergent. The necessity of holomorphic nondegeneracy was known previously. Our technique is an adaptation of the inductional study of the jets of formal CR maps which was discovered by Baouendi-Ebenfelt-Rothschild. However, as the manifolds we consider are far from being finitely nondegenerate, we must consider some newconjugate reflection identitieswhich appear to be crucial in the proof. The higher codimensional case will be studied in a forthcoming paper.

scholarly journals Convergent normal form for real hypersurfaces at a generic Levi-degeneracy

2019 ◽  
Vol 2019 (749) ◽  
pp. 201-225
Author(s):  
Ilya Kossovskiy ◽  
Dmitri Zaitsev
Keyword(s):  
Normal Form ◽  
Moduli Space ◽  
Real Hypersurface ◽  
Convergence Result ◽  
Explicit Description ◽  
Real Hypersurfaces ◽  
Real Analytic ◽  
Real Analytic Hypersurfaces

Abstract We construct a complete convergent normal form for a real hypersurface in {\mathbb{C}^{N}} , {N\geq 2} , at a generic Levi-degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. As an application of the convergence result, we obtain an explicit description of the moduli space of germs of real-analytic hypersurfaces with a generic Levi-degeneracy. As another application, we obtain, in the spirit of the work of Chern and Moser [6], distinguished curves inside the Levi-degeneracy set that we call degenerate chains.

Algebraicity of Global Real Analytic Hypersurfaces

2006 ◽  
Vol 119 (1) ◽  
pp. 141-149 ◽  
Author(s):  
Wojciech Kucharz ◽  
Krzysztof Kurdyka
Keyword(s):  
Real Analytic ◽  
Real Analytic Hypersurfaces
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