Universality limits involving orthogonal polynomials on a smooth closed contour

We establish universality limits for measures on a smooth closed contour Γ in the plane. Assume that μ is a regular measure on Γ, in the sense of Stahl, Totik, and Ullmann. Let Γ₁ be a closed subarc of Γ, such that μ is absolutely continuous in an open arc containing Γ₁, and μ^′ is positive and continuous in that open subarc. Then universality for μ holds in Γ₁, in the sense that the reproducing kernels (K_n (z, t)) for μ satisfy (Formula Presented) uniformly for z₀ ∈ Γ₁, and s, t in compact subsets of the complex plane. Here (Formula Presented) is the sinc kernel, and ф is a conformal map of the exterior of Γ onto the exterior of the unit ball.