On quasiconformal mappings which keep the boundary points fixed

Abstract

Introduction. From a variational point of view it is natural to consider quasiconformal selfmappings of a domain which are equal to the identity on the boundary. We say that a function i in the unit disk U={z | \z\ < 1} belongs to the class J*" if and only if it is the complex dilatation of a quasiconformal selfmapping/of U which satisfies f(ew) = eie, 0^0<2w.