Quasi-reflections, Fredholm eigenvalues and Finsler metrics

The aim of the paper is to present a new method for solutions of the problems of quasi-reflection, Fredholm eigenvalues and Finsler metrics. This method permits to solve these problems for the wide classes of convex regions and fractional-linear images. The developed method is based on using the complex geometry of the Tykhemueller universal space T and the Finsler metrics on holomorphic disks in T. The properties of holomorphic motions along these disks are used too.