# 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}
}
• Published 5 September 2018
• Mathematics
• Complex Analysis and its Synergies
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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