Common fixed points of commuting holomorphic maps in the unit ball of Cn

Let B-n be the unit ball of C-n (n > 1). We prove that if f, g is an element of Hol(B-n, B-n) are holomorphic self-maps of B-n such that f circle g = g circle f, then f and g have a common fixed point (possibly at the boundary, in the sense of K-limits). Furthermore, if f and g have no fixed points in B-n, then they have the same Wolff point, unless the restrictions of f and g to the one-dimensional complex affine subset of B-n determined by the Wolff points of f and g are commuting hyperbolic automorphisms of that subset.