Value ranges of univalent self-mappings of the unit disc

摘要

We describe the value set {f(z(0)) vertical bar f : D -> D univalent, f(0) = 0, f '(0) = e(-T)} where D denotes the unit disc and z(0) is an element of D {0}, T > 0, by applying Pontryagin's maximum principle to the radial Loewner equation. (C) 2015 Elsevier Inc. All rights reserved.