Semi-global extension of maximally complex submanifolds
  Let A be a domain of the boundary of a strictly pseudoconvex domain \Omega of C^n and M a smooth, closed, maximally complex submanifold of A. We find a subdomain \widetilde A of \Omega, depending only on \Omega and A, and a complex subvariety W of \widetilde A such that bW\cap A = M. Moreover, a generalization to analytic sets of depth at least 4 is given. 
Giuseppe Della Sala, Alberto Saracco