Anderson's Conjecture and Radial Variation of Bloch Functions

In 1971 J.M. Anderson conjectured that for any

conformal map

in the unit disc there exists

SRC="1998_02_03_688/img7.gif">

such that

More recently this problem has been posed in the works of N. Makarov,

Ch. Pommerenke and D. Gnuschke - Ch. Pommerenke. The purpose of the present

talk is to prove Anderson's conjecture. This will be done by

showing the following theorem about the associated Bloch function