COMPLEX GEODESICS AND ITERATES OF HOLOMORPHIC MAPS ON CONVEX DOMAINS IN C(N)

We study complex geodesics f: DELTA --> OMEGA, where DELTA is the unit disk in C and OMEGA belongs to a class of bounded convex domains in C(n) with no boundary regularity assumption. Along with continuity up to the boundary, existence of such complex geodesics with two prescribed values z, omega is-an-element-of OMEGABAR is established. As a consequence we obtain some new results from iteration theory of holomorphic self maps of bounded convex domains in C(n) .