On bounded univalent functions and the angular derivative (Q2769223)

In this beautiful paper the authors study bounded univalent functions \(f\) that map the unit disk into itself such \(f(0)=0\). In particular, they are interested in the study of functions for which the angular derivative and the angular limit exist at certain points on the unit circle. For such functions, the authors obtain interesting estimates, most of them are sharp. To this end, they use two different methods: one is based on the Schiffer-Tammi analogue of the Grusky inequality, and the other uses the method of modules of curve families and the extremal partition of domains.