Some open problems

Abstract

As we have seen in Chapter 6 it is a very difficult task to find sharp punishing factors or substitutes for them in cases where multiply connected domains are involved. From this point of view, it seems natural that the difficulties become nearly insuperable, if one allows the points z0 ∈ Ω or f(z0) ∈ Π, or both to vary, and asks for the maximum. Nevertheless, there exists one problem of this type that has attracted researchers for many years because of the conjectured simple solution. This is the so-called Krzyż conjecture. 2009 Birkhäuser Verlag AG.