Value ranges of univalent self-mappings of the unit disc

We describe the value set {f(z0)|f:D→D univalent,f(0)=0,f′(0)=e−T}, where DD denotes the unit disc and z0∈D∖{0}z0∈D∖{0}, T>0T>0, by applying Pontryagin's maximum principle to the radial Loewner equation.