Semi-global extension of maximally complex submanifolds
arXiv:math/0607747
Abstract
Let A be a domain of the boundary of a strictly pseudoconvex domain Ωof C^n and M a smooth, closed, maximally complex submanifold of A. We find a subdomain \widetilde A of Ω, depending only on Ωand 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.
16 pages, v2 example modified and generalization to analytic sets (sec. 5) added