The Riemann-Hilbert Problem on the Riemann Surface

Abstract

Here we reduce Eq. (15.11) to the Riemann-Hilbert problem. Let us recall that the function $\hat v_{21}$ is meromorphic in $\varPi _{-2\varPhi }^\pi$ by (15.9) and Lemma 15.2. Consider the strip

$$\displaystyle W:=\varPi _{\pi -2\varPhi }^\pi .$$