Flattening of CR singular points and analyticity of the local hull of holomorphy I

@article{Huang2012FlatteningOC,
  title={Flattening of CR singular points and analyticity of the local hull of holomorphy I},
  author={Xiaojun Huang and Wanke Yin},
  journal={Mathematische Annalen},
  year={2012},
  volume={365},
  pages={381-399}
}
This is the first article of the two papers in which we investigate the holomorphic and formal flattening problem for a codimension two real submanifold in $${\mathbb C}^n$$Cn with $$n\ge 3$$n≥3 near a non-degenerate CR singular point. The problem is motivated from the study of the complex Plateau problem that seeks for the Levi-flat hypersurface bounded by a given real submanifold and is motivated by the classical complex analysis problem of finding the local hull of holomorphy of a real… 
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20 Citations
Background Citations
2
Methods Citations
2
Results Citations
2

20 Citations

Citation Type

Citation Type

Flattening of CR singular points and analyticity of the local hull of holomorphy II
Flattening a non-degenerate CR singular point of real codimension two
This paper continues the previous studies in two papers of Huang–Yin [HY16,HY17] on the flattening problem of a CR singular point of real codimension two sitting in a submanifold in $${{\mathbb…
CR singular images of generic submanifolds under holomorphic maps
The purpose of this paper is to organize some results on the local geometry of CR singular real-analytic manifolds that are images of CR manifolds via a CR map that is a diffeomorphism onto its…
NORMAL FORMS FOR CR SINGULAR CODIMENSION TWO LEVI-FLAT SUBMANIFOLDS
Real-analytic Levi-flat codimension two CR singular submanifolds are a natural generalization to C m , m > 2, of Bishop surfaces in C 2 . Such submanifolds for example arise as zero sets of…
Real submanifolds of maximum complex tangent space at a CR singular point, I
We study a germ of real analytic n-dimensional submanifold of $${\mathbf {C}}^n$$Cn that has a complex tangent space of maximal dimension at a CR singularity. Under some assumptions, we show its…
Geometric and analytic problems for a real submanifold in ℂn with CR singularities
In this survey article, we present some known results and also propose some open questions related to the analytic and geometric aspects of Bishop submanifolds in a complex space. We mainly focus on…
On the Levi-flat Plateau problem
We solve the Levi-flat Plateau problem in the following case. Let $$M \subset {\mathbb {C}}^{n+1}$$ M ⊂ C n + 1 , $$n \ge 2$$ n ≥ 2 , be a connected compact real-analytic codimension-two submanifold…
A CR singular analogue of Severi’s theorem
Real-analytic CR functions on real-analytic CR singular submanifolds are not in general restrictions of holomorphic functions, unlike in the CR nonsingular case. We give a simple condition that…
Codimension Two CR Singular Submanifolds and Extensions of CR Functions
Let $$M \subset {\mathbb {C}}^{n+1}$$M⊂Cn+1, $$n \ge 2$$n≥2, be a real codimension two CR singular real analytic submanifold that is nondegenerate and holomorphically flat. We prove that every real…
Convergence of the Chern–Moser–Beloshapka normal forms
Abstract In this article, we give a normal form for real-analytic, Levi-nondegenerate submanifolds of ℂN{\mathbb{C}^{N}} of codimension d≥1{d\geq 1} under the action of formal biholomorphisms. We…
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