THE AHLFORS MAPPING FUNCTION AND AN EXTREMAL PROBLEM IN THE PLANE

Suppose that OMEGA is a bounded n-connected domain in the plane with C(infinity) smooth boundary and let SIGMA be the family of holomorphic functions h of OMEGA into the unit disc in the plane, with h(zeta) = h'(zeta) = 0. Suppose that the Ahlfors map f(zeta) has distinct zeros at z = zeta, a1,...,a(n-1). There exist constants c(j), j = 1,...,n-1, depending on zeta, which are conformally invariant, such that for any function h is-an-element-of SIGMA [GRAPHICS]