Let S be the usual class of univalent functions in {|z| < 1} normalized by f(z) = z + sumfromi=2toinf asubizsupi and Vsubn the coefficient region of S. It is well known that f corresponds to a boundary point of Vsubn if and only if f satisfies a quadratic equation of the form Q(w)dwsup2 = R(z)dzsup2 called Schiffers equation that maps {|z| < 1} onto a slit domain. We treat the following problems numerically for Vsub4:

1. Given Q find R and f.
2. Find the function that maximizes Re esupisupphi asub4 with theconstraint that asub2 and asub3 are some given complex numbers in Vsub3. In this case Schiffers equation is a sufficient condition for f to be extremal. The critical trajectories of Q(w)dwsup2 and R(z)dzsup2 are in each case displayed graphically for some particular examples.