The global parametrix in the Riemann-Hilbert steepest descent analysis for orthogonal polynomials

In the application of the Deift-Zhou steepest descent method to the Riemann-Hilbert problem for orthogonal polynomials, a model Riemann-Hilbert problem that appears in the multi-cut case is solved with the use of hyperelliptic theta functions. We present here an alternative approach which uses meromorphic differentials instead of theta functions to construct the solution of the model Riemann-Hilbert problem.