The Riemann–Hilbert problem for certain poly domains and its connection to the Riemann problem

The Riemann–Hilbert problem is studied for holomorphic functions in higher dimensional poly domains and the explicit constructive solution is given. The connection between the Riemann problem and the Riemann–Hilbert problem for poly domains is presented and proven. Contrary to earlier studies, our results provide explicit solutions and are not attached to any artificial assumptions.