  An important open problem in geometric complex analysis is to find algorithms
for explicit determination of basic functionals intrinsically connected with
conformal and quasiconformal maps, such as their Teichmuller and Grunsky norms,
Fredholm eigenvalues and the quasireflection coefficient. This has not been
solved even for convex polygons. This case has intrinsic interest in view of
the connection of such polygons with the geometry of the universal Teichmuller
space.
  We provide a new approach, based on affine transformations of univalent
functions.
