On the Levi-flat Plateau problem

@article{Lebl2020OnTL,
  title={On the Levi-flat Plateau problem},
  author={Jiř{\'i} Lebl and Alan V. Noell and Sivaguru Ravisankar},
  journal={Complex Analysis and its Synergies},
  year={2020},
  volume={6},
  pages={1-15}
}
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 with only nondegenerate CR singularities. Suppose M is a diffeomorphic image via a real-analytic CR map of a real-analytic hypersurface in $${\mathbb {C}}^n \times {\mathbb {R}}$$ C n × R with only nondegenerate CR singularities. Then there exists a unique compact real-analytic Levi-flat… 
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References

SHOWING 1-10 OF 16 REFERENCES
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
Boundary problem for Levi flat graphs
In an earlier paper the authors provided general conditions on a real codimension 2 submanifold $S\subset C^{n}$, $n\ge 3$, such that there exists a possibly singular Levi-flat hypersurface $M$
Extension of CR functions from boundaries in ${\mathbb C}^n \times {\mathbb R}$
Let $\Omega \subset {\mathbb C}^n \times {\mathbb R}$ be a bounded domain with smooth boundary such that $\partial \Omega$ has only nondegenerate elliptic CR singularities, and let $f \colon \partial
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 $${{\mathbb
Flattening of CR singular points and analyticity of the local hull of holomorphy I
This is the first article of the two papers in which we investigate the holomorphic and formal flattening problem for a codimension two real submanifold in $${\mathbb C}^n$$Cn with $$n\ge 3$$n≥3 near
On a problem of Moser
1 0 Introduction This paper studies the analytic structure of the local hull of holomorphy of a 2-dimensional, real analytic manifold that is embedded in C 2. Our specific purpose is to solve a
On Lewy extension for smooth hypersurfaces in ℂⁿ×ℝ
TLDR
An analogue of the Lewy extension theorem for a real dimension is proved and the theorem implies that if if if, then n times double-struck upper R.
Levi flat hypersurfaces in $C^2$ with prescribed boundary : stability
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions
...
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