Abstract: I will talk about the extension of CR functions and its application to a certain solution of the so-called Levi-flat Plateau problem. The classical Plateau problem asks for a minimal surface like soap film attached to a bent wire. In our setting we are asking for a Levi-flat hypersurface. A Levi-flat hypersurface in ${\mathbb C}^n$ is a real hypersurface foliated by complex hypersurfaces. The Plateau problem asks for such a hypersurface given a boundary. This is joint work with Alan Noell and Sivaguru Ravisankar.
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