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A note on a family of analytic discs attached to a real submanifold M ⊂ C N + 1 with a CR singularity

  title={A note on a family of analytic discs attached to a real submanifold M ⊂ C N + 1 with a CR singularity},
  author={Valentin Burcea},
In this note we construct a family of analytic discs attached to a real submanifold M ⊂ CN+1 of codimension 2 with a CR singularity. These discs are mutually disjoint and form a smooth hypersurface M̃ with boundary M in a neighborhood of the CR singularity. As an application we prove that if p is a flat-elliptic CR singularity and if M is nowhere minimal at its CR points and does not contain a complex manifold of dimension (n − 2) then M̃ is a Levi-flat hypersurface real-analytic across the… 
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