Differentiability properties of some nonlinear operators associated to the conformal welding of Jordan curves in Schauder spaces (Q1409326)

It is well-known that to a simple closed sufficiently smooth curve of the complex plane a conformal welding homeomorphism of the unit disk onto itself is given by composing the conformal mapping of the interior and the exterior of the unit disk onto the interior and the exterior of the domain given by the simple closed curve. The inverse problem to construct a pair of suitably normalized functions for a given regular homeomorphism of the unit disk onto itself is called conformal sewing. The paper deals with differentiability properties of this conformal welding and conformal sewing homeomorphisms. It should be mentioned that sewing theorems are used extensively by P. Koebe. For the Riemann-Hilbert problem the authors use the unusual name Haseman problem which is not justified (compare Haseman's thesis, Göttingen 1907).