Riemann-Hilbert problems of the theory of automorphic and algebraic functions and an inverse problem of elasticity for multiply connected domains

Professor Yuri Antipov (Louisiana State University, Baton Rouge, visiting Isaac Newton Institute, Cambridge). Part of the Analysis and Applications Seminar Series.

The theory of two Riemann-Hilbert problems is revised. The first one concerns piece-wise holomorphic automorphic functions generated by the Schottky symmetry groups, while the second problem is set for piece-wise holomorphic functions on Riemann surfaces of algebraic functions. In terms of the solutions to these problems, certain conformal mappings are constructed. The maps serve for the solution of nonlinear inverse problems of elasticity for multiply connected domains. Specifically, the problem of determining the profiles of n uniformly stressed inclusions when the surrounding infinite body is subjected to antiplane uniform shear at infinity is studied.