Value range of solutions to the chordal Loewner equation

We describe a value range {f(z0)} over the class of holomorphic univalent mappings from H∖K(T) onto the upper half-plane H with the hydrodynamic normalization at infinity where K(T) is an arbitrary hull of half-plane capacity T>0. Without loss of generality choose z0=i. A similar value range over the class of inverse functions f−1 is also described. This is a specification of the result by Roth and Schleissinger.