The Denjoy–Wolff theorem in CnCn

If DD is a bounded and strictly convex domain in CnCn and f:D→Df:D→D is holomorphic and fixed-point-free, then there exists ξ̃∈∂D such that the sequence {fn}{fn} of the iterates of ff converges in the compact–open topology to the constant mapping taking the value ξ̃.