Bulletin of the
Korean Mathematical Society BKMS

In this note we study more about the omitted arc for the extremal functions and its $\pi \over 4$-property based upon Schiffer's variational method and Brickman-Wilken's result. We give an example other than the Koebe function which is both a support point of $S$ and the extreme point of $HS$. Furthermore, we discuss the relations between the support points and the L\"owner chain.

Keywords: slit mapping, trajectories, support points, extreme points

MSC numbers: Primary 30C45