  An important problem in applications of quasiconformal analysis and in its
numerical aspect is to establish algorithms for explicit or approximate
determination of the basic quasiinvariant curvelinear and analytic functionals
intrinsically connected with conformal and quasiconformal maps, such as their
Teichmuller and Grunsky norms, Fredholm eigenvalues and the quasireflection
coefficients of associated quasicircles.
  We prove a general theorem of new type answering this question for univalent
functions in arbitrary quasiconformal domains and provide its applications. The
results are strengthened in the case of maps of the disk and give rise to
extremal Beltrami coefficients of a new type.
