Riemann-Hilbert problems of the theory of automorphic functions and inverse problems of elasticity and cavitating flow for multiply connected domains

The general theory of the Riemann-Hilbert problem for piece-wise holomorphic automorphic functions generated by the Schottky symmetry groups is discussed.  The theory is illustrated by two inverse problems for multiply connected domains. The first one concerns the determination of the profiles on n inclusions in an elastic plane subjected to shear loading at infinity when the stress field in the inclusions is uniform. The second problem is a model problem of cavitating flow past n hydrofoils. Both problems are solved by the method of conformal mappings. The maps from n-connected circular domain into the physical domain are reconstructed by solving two Riemann-Hilbert problems of the theory of piece-wise holomorphic automorphic functions.