Abstract: I will describe a result by Eliashberg and Polterovich that allows to construct a family $J_n$ of complex structures on $T^2\times D^2$ with strictly pseudoconvex boundary which are biholomorphically equivalent and homotopic through complex structures but not homotopic through complex structures with strictly pseudoconvex boundary. Note: $T^2\times D^2$ denotes the product of the 2-torus and the closed unit disk in $R^2$. The proof is based on the Lagrangian surgery method of K. Luttinger.