Inner Radius of Univalence for a Strongly Starlike Domain

Abstract

The inner radius of univalence of a domain D with Poincare density ρD is the possible largest number σ such that the condition ∥ Sf ∥D = supw∈ D ρD (w)−2∥ Sf (z) ∥ ≤ σ implies univalence of f for a nonconstant meromorphic function f on D, where Sf is the Schwarzian derivative of f. In this note, we give a lower bound of the inner radius of univalence for strongly starlike domains of order α in terms of the order α.