Value range of solutions to the chordal Loewner equation

We describe a value range {f(z(0))} over the class of holomorphic univalent mappings from H\K(T) onto the upper half-plane IHI with the hydrodynamic normalization at infinity where K(T) is an arbitrary hull of half-plane capacity T > 0. Without loss of generality choose z(0) = 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. (C) 2015 Elsevier Inc. All rights reserved.