A coefficient problem for univalent functions related to two-point distortion theorems

We discuss a class of coefficient functionals over the set of normalized un ivalent functions on the unit disk. These functionals are related to symmet ric, linearly invariant two-point distortion theorems for univalent functio ns due to Kim and Minda. Each of these theorems is necessary and sufficient for univalence. A special case is a distortion theorem of Blatter. Our app roach is based on an application of Pontryagin's maximum principle to the L oewner differential equation. In the same fashion, two-point distortion the orems for bounded univalent functions are obtained. Related coefficient fun ctionals are discussed, too.