Assume that is a \(\varOmega \) bounded, strictly pseudoconvexed domain with \(C^{2}\) boundary. Let \(D\subset \mathbb {C}^{n}\) be a bounded strictly convex domain in a geometric sense, i.e. D is bounded and convex without any line segment in the boundary. If n is large enough, then there exists a proper holomorphic embedding \(f:\varOmega \rightarrow D\) , which extends continuously through \(\overline{\varOmega }\) .
