HAUSDORFF DIMENSION OF JULIA SETS OF UNICRITICAL CORRESPONDENCES

We show that if ,Q > 1 is a rational number and the Julia set J of the holomorphic correspondence z beta + c is a locally eventually onto hyperbolic repeller, then the Hausdorff dimension of J is bounded from above by the zero of the associated pressure function. As a consequence, we conclude that the Julia set of the correspondence has zero Lebesgue measure for parameters close to zero, whenever q2 < p and ,Q = p/q in lowest terms.