Anderson's Conjecture and Radial Variation of Bloch Functions

In 1971 J.M. Anderson conjectured that for any conformal map 𝜑 in the unit disc there exists β,0 ≤ β ≤ 2π 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 b = log|𝜑'|.