 More generally, "U" and "V" can be complex manifolds.As in the case of functions of a single complex variable, a sufficient condition for a holomorphic map to be biholomorphic onto its image is that the map is injective, in which case the inverse is also holomorphic (e.g., see Gunning 1990, Theorem I.11).If there exists a biholomorphism formula_5, we say that "U" and "V" are biholomorphically equivalent or that they are biholomorphic.