Levi-flat hypersurfaces with real analytic boundary

  title={Levi-flat hypersurfaces with real analytic boundary},
  author={Jiř{\'i} Lebl},
  journal={Transactions of the American Mathematical Society},
  • Jiří Lebl
  • Published 19 October 2007
  • Mathematics
  • Transactions of the American Mathematical Society
Let X be a Stein manifold of dimension at least 3. Given a compact codimension 2 real analytic submanifold M of X, that is the boundary of a compact Levi-flat hypersurface H, we study the regularity of H. Suppose that the CR singularities of M are an O(X)-convex set. For example, suppose M has only finitely many CR singularities, which is a generic condition. Then H must in fact be a real analytic submanifold. If M is real algebraic, it follows that H is real algebraic and in fact extends past… 

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