UNIVALENT FUNCTIONS AND RADIAL GROWTH

We address a question raised by Anderson, Hayman and Pommerenke relating to a classical result on univalent functions f in the unit disc due to Spencer, and involving the size of the set of θ ∈ [ ‐ π , π ] for which we havelog | f ( r e i θ ) | ≠ o ( log ( 1 / ( 1 ‐ r ) ) )as r → 1 . An answer is given in terms of a certain generalized capacity, and also in terms of Hausdorff measure. Further results regarding the radial growth of univalent functions are also established, and some examples are constructed which relate to the sharpness of these results.