The harmonic mapping whose Hopf differential is a constant

Suppose that h(z) is a harmonic mapping from the unit disk D to itself with respect to the hyperbolic metric. If the Hopf differential of h(z) is a constant c > 0, the Beltrami coefficient μ(z) of h(z) is radially symmetric and takes the maximum at z = 0. Furthermore, the mapping γ: c → μ(0) is increasing and gives a homeomorphism from (0,+∞) to (0, 1).