Multiplicity, regularity and lipschitz geometry of real analytic hypersurfaces

2021 ◽  
Author(s):  
José Edson Sampaio
Keyword(s):  
Real Analytic ◽  
Real Analytic Hypersurfaces

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

scholarly journals Parametrization of local biholomorphisms of real analytic hypersurfaces

1997 ◽  
Vol 1 (1) ◽  
pp. 1-16 ◽  
Author(s):  
M. S. Baouendi ◽  
P. Ebenfelt ◽  
Linda Preiss Rothschild
Keyword(s):  
Real Analytic ◽  
Real Analytic Hypersurfaces

scholarly journals ON THE CLASSIFICATION BY MORIMOTO AND NAGANO

2019 ◽  
pp. 1-13
Author(s):  
ALEXANDER ISAEV
Keyword(s):  
Three Dimensional ◽  
Parameter Range ◽  
Real Hypersurfaces ◽  
Polynomial Map ◽  
Real Analytic ◽  
Cauchy Riemann ◽  
Real Analytic Hypersurfaces ◽  
Simply Connected

We consider a family $M_{t}^{3}$ , with $t>1$ , of real hypersurfaces in a complex affine three-dimensional quadric arising in connection with the classification of homogeneous compact simply connected real-analytic hypersurfaces in $\mathbb{C}^{n}$ due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the Cauchy–Riemann (CR)-embeddability of $M_{t}^{3}$ in $\mathbb{C}^{3}$ . In our earlier article, we showed that $M_{t}^{3}$ is CR-embeddable in $\mathbb{C}^{3}$ for all $1<t<\sqrt{(2+\sqrt{2})/3}$ . In the present paper, we prove that $M_{t}^{3}$ can be immersed in $\mathbb{C}^{3}$ for every $t>1$ by means of a polynomial map. In addition, one of the immersions that we construct helps simplify the proof of the above CR-embeddability theorem and extend it to the larger parameter range $1<t<\sqrt{5}/2$ .

Sign in / Sign up

Export Citation Format

Share Document