On Fredholm Eigenvalues of Unbounded Polygons

Abstract

An important open problem in geometric complex analysis is to establish some algorithms for explicit determination of the basic functionals intrinsically connected with conformal and quasiconformal mappings such as their Teichmüller and Grunsky norms, Fredholm eigenvalues and the quasireflection coefficient. This problem has not been solved even for generic quadrilaterals. We provide a restricted solution of the problem for unbounded rectilinear polygons.