Embedding univalent functions in filtering Loewner chains in higher dimension

We discuss the problem of embedding univalent functions into Loewner chains in higher dimension. In particular, we prove that a normalized univalent map of the ball in ℂn whose image is a smooth strongly pseudoconvex domain is embeddable into a normalized Loewner chain (also satisfying some extra regularity properties) if and only if the closure of the image is polynomially convex.